Preliminary NPB Model for Birth Weight
Sheena Martenies
07/21/2020
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#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)
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## date, intersect, setdiff, unionlibrary(haven)
library(readxl)
library(mmpack)
#' For ggplots
simple_theme <- theme(
#aspect.ratio = 1,
text = element_text(family="Calibri",size = 12, color = 'black'),
panel.spacing.y = unit(0,"cm"),
panel.spacing.x = unit(0.25, "lines"),
panel.grid.minor = element_line(color = "transparent"),
panel.grid.major = element_line(color = "transparent"),
panel.border=element_rect(fill = NA),
panel.background=element_blank(),
axis.ticks = element_line(colour = "black"),
axis.text = element_text(color = "black", size=10),
# legend.position = c(0.1,0.1),
plot.margin=grid::unit(c(0,0,0,0), "mm"),
legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notationIn this version of the analysis, we wanted to try a few things to refine our model and check some things out. After meeting with Ander, Lauren, and Sheryl, here’s what we’ve come up with:
- The effect of ozone seen in the previous version of the model might actually be a seasonal signal. I’m going to add indicator variables for season of conception
- Residual spatial confounding is also an issue given the spatial patterns in both the environmental (esp. ozone) and social exposures. We’re addressing this in two ways:
- First, we’re adding lon, lat, and lon*lat to the covariates matrix
- Second, we’re adding census tract percent POC (Total Pop - NHW / Total Pop * 100) to the exposures
- In order to better compare the RIDGE and NPB models, I’m generating rescaled estimates and 95% CIs for the RIDGE coefficients
We also wanted to try rerunning the BKMR model with exposures selected by the NPB model. If we have 3 predictors with a PIP > 0.5 (or close to it), we can include them in a BKMR. Alternatively, for 1-2 exposures, we can just look at a GAM
Lauren is going to add a frame to the summary() function that will give us posterior means and CIs for the covariates (but they won’t have PIPs)
1 Exploring the data set
The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.
The complete data set for the birth weight outcome consists of n = 897 participants. This represents 77.93% of the original Healthy Start 1 cohort.
Of the 897 participants, 27% identify as Latina, 17% identify as Black, and 27% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 51% of babies born were male.
1.1 Effect of year on birth weight
In models below, Ander noticed an effect of year of conception on birth weight. Conception year was included in models below as dummy variables. I’m not sure why this effect exists. Here I am plotting birth weight against date of birth. The trend line ever so slighly increases over time.
plot(hs_data1$dob, hs_data1$birth_weight)
abline(lm(birth_weight ~ dob, data = hs_data1), col = "red")
Grouping birth weights by conception year doesn’t show much of a trend:
bw_trends_by_concept <- ggplot(data = hs_data1) +
geom_boxplot(aes(x = concep_year, group = concep_year, y = birth_weight))
bw_trends_by_concept## Warning: Removed 5 rows containing non-finite values (stat_boxplot).
1.2 Exposure data
We have included 19 exposures in our analysis.
These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3), these are based on long-term averages at for each census tract. For mean_pm and mean_o3 are based on the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,] 8.483046 47.19072 6.006276 43.30893 10128.4962
## [2,] 6.598608 50.05090 7.281109 48.36432 10749.0359
## [3,] 7.454146 48.57052 17.205991 31.67281 9048.6468
## [4,] 6.671239 50.06429 6.842898 45.00359 4223.3434
## [5,] 7.122537 50.14275 3.357792 28.16745 858.7283
## [6,] 7.637453 47.03125 10.743612 45.87564 15603.9800
## dist_m_tri dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,] 2827.538 729.2371 4829.780 7968.654 29116.58
## [2,] 1576.420 5239.2211 4417.792 3780.951 51044.30
## [3,] 3350.303 2992.2968 5211.871 7423.232 36079.21
## [4,] 3364.954 6998.1286 8921.318 9636.816 42235.78
## [5,] 2923.811 3427.2247 7006.042 6806.912 29145.98
## [6,] 3364.200 3166.5395 4484.960 5265.285 43921.85
## dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,] 1749.1256 275.2480 155.7767 14.377133
## [2,] 7354.5310 279.6435 226.8038 8.905404
## [3,] 4887.2996 221.0414 157.6974 7.636888
## [4,] 3752.6399 203.8812 142.5368 2.850212
## [5,] 729.7784 194.1983 101.0046 5.435988
## [6,] 5870.6867 174.3361 120.3281 5.035971
## property_crime_rate pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## [1,] 37.32935 31.784946 11.529628 26.114650 12.010919
## [2,] 67.03932 15.290231 4.908306 8.500401 18.123496
## [3,] 46.78194 6.891702 4.564963 0.000000 6.307978
## [4,] 21.95270 2.725915 5.623583 1.350621 9.292274
## [5,] 22.49834 12.919186 5.234103 6.307385 2.115768
## [6,] 47.15500 3.842365 10.000000 5.121799 25.171768
## pct_poc
## [1,] 90.33703
## [2,] 30.44025
## [3,] 26.63305
## [4,] 32.68648
## [5,] 73.60772
## [6,] 23.08698Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 pct_tree_cover
## mean_pm 0.391784015 0.006083605 -0.2054297
## mean_o3 0.006083605 9.383489039 -0.4158151
## pct_tree_cover -0.205429726 -0.415815089 9.7193077
## pct_impervious 0.508898445 -1.674151031 5.8719893
## mean_aadt_intensity -182.234953786 474.627052967 8431.6446632
## dist_m_tri -255.176839682 444.286548683 -73.1423054
## dist_m_npl -289.002141382 539.849185829 434.4654007
## dist_m_waste_site -275.262105884 261.902915064 1933.8647304
## dist_m_major_emit 71.096593638 577.257325397 265.4284518
## dist_m_cafo -1291.237441927 -35.275020052 10170.6234275
## dist_m_mine_well -339.250592215 -375.434990683 3136.3680766
## cvd_rate_adj 3.871688575 0.939328342 -24.8232924
## res_rate_adj 2.356328835 -0.181515705 -3.5331376
## violent_crime_rate 0.232839920 0.577648302 -4.0583754
## property_crime_rate 2.001989749 -2.773092354 -22.6429724
## pct_less_hs 1.132232861 0.637361326 -7.5753471
## pct_unemp 0.100439902 0.288530482 -0.3330523
## pct_limited_eng 0.432516169 0.295617023 -2.8349116
## pct_hh_pov 0.731824476 -0.606648513 0.3805472
## pct_poc 1.632059580 1.202932299 -19.4091792
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.5088984 -182.2350 -255.17684
## mean_o3 -1.6741510 474.6271 444.28655
## pct_tree_cover 5.8719893 8431.6447 -73.14231
## pct_impervious 176.8316214 55459.6063 -15279.44024
## mean_aadt_intensity 55459.6063235 67283287.0201 -1315386.69307
## dist_m_tri -15279.4402428 -1315386.6931 6558190.20296
## dist_m_npl -7729.3843793 1683196.0799 4282727.94125
## dist_m_waste_site -4662.9983638 2039577.9230 2441267.84540
## dist_m_major_emit 2627.0270993 2477155.3406 1433153.16531
## dist_m_cafo 16586.9964129 15462371.9832 3431065.70215
## dist_m_mine_well 706.6674650 2073244.5987 995872.11873
## cvd_rate_adj 230.4542985 20477.4374 -49347.60273
## res_rate_adj 176.8108084 33055.3733 -31870.98664
## violent_crime_rate 26.6945028 5736.5627 -1014.08753
## property_crime_rate 118.0737725 22077.3894 -5365.69285
## pct_less_hs 56.8383947 -4056.6889 -12372.14262
## pct_unemp 25.9434246 6003.3343 -2527.22451
## pct_limited_eng 41.9919053 2620.6198 -5408.86434
## pct_hh_pov 82.2198624 17850.1649 -8842.76408
## pct_poc 88.3560154 4526.2710 -18049.42332
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -289.0021 -275.2621 71.09659
## mean_o3 539.8492 261.9029 577.25733
## pct_tree_cover 434.4654 1933.8647 265.42845
## pct_impervious -7729.3844 -4662.9984 2627.02710
## mean_aadt_intensity 1683196.0799 2039577.9230 2477155.34057
## dist_m_tri 4282727.9413 2441267.8454 1433153.16531
## dist_m_npl 11125411.7474 4193498.0586 6948817.25739
## dist_m_waste_site 4193498.0586 5344101.7540 1395277.06805
## dist_m_major_emit 6948817.2574 1395277.0681 10114549.72263
## dist_m_cafo 5416531.1320 5586018.8251 -2993791.05377
## dist_m_mine_well 256924.3029 1375784.7856 -1810174.74785
## cvd_rate_adj -30921.0390 -43119.5785 16272.40152
## res_rate_adj -19393.1304 -32402.8440 -1320.21297
## violent_crime_rate -672.9264 -3702.6112 -360.49700
## property_crime_rate -18283.4264 -22350.3006 -24007.42305
## pct_less_hs -6760.5337 -11422.4985 8866.74917
## pct_unemp 2195.0515 -1476.4094 5212.74830
## pct_limited_eng 498.0033 -4277.8134 9367.28435
## pct_hh_pov -1135.3843 -7599.7432 8682.26135
## pct_poc -1456.8941 -8602.8521 22698.24353
## dist_m_cafo dist_m_mine_well cvd_rate_adj
## mean_pm -1291.23744 -339.2506 3.8716886
## mean_o3 -35.27502 -375.4350 0.9393283
## pct_tree_cover 10170.62343 3136.3681 -24.8232924
## pct_impervious 16586.99641 706.6675 230.4542985
## mean_aadt_intensity 15462371.98316 2073244.5987 20477.4373759
## dist_m_tri 3431065.70215 995872.1187 -49347.6027339
## dist_m_npl 5416531.13199 256924.3029 -30921.0389720
## dist_m_waste_site 5586018.82514 1375784.7856 -43119.5785165
## dist_m_major_emit -2993791.05377 -1810174.7478 16272.4015197
## dist_m_cafo 46324000.89481 9345575.3772 -46645.9665229
## dist_m_mine_well 9345575.37722 4430024.9964 -39046.5984701
## cvd_rate_adj -46645.96652 -39046.5985 2039.8569530
## res_rate_adj -13772.40263 -16322.5110 1289.5661935
## violent_crime_rate 722.31907 -2032.3464 135.9487143
## property_crime_rate -15833.92381 -4272.3829 343.9364726
## pct_less_hs -26060.83378 -10037.6577 328.3044447
## pct_unemp -1030.96916 -2827.2369 105.0153846
## pct_limited_eng -7089.15821 -4814.6687 183.5853966
## pct_hh_pov -855.38016 -5030.4055 266.1004715
## pct_poc -44526.37107 -24974.3303 618.2817294
## res_rate_adj violent_crime_rate property_crime_rate
## mean_pm 2.3563288 0.2328399 2.001990
## mean_o3 -0.1815157 0.5776483 -2.773092
## pct_tree_cover -3.5331376 -4.0583754 -22.642972
## pct_impervious 176.8108084 26.6945028 118.073773
## mean_aadt_intensity 33055.3733277 5736.5627383 22077.389365
## dist_m_tri -31870.9866403 -1014.0875345 -5365.692846
## dist_m_npl -19393.1304345 -672.9263612 -18283.426420
## dist_m_waste_site -32402.8439544 -3702.6111771 -22350.300554
## dist_m_major_emit -1320.2129699 -360.4970006 -24007.423046
## dist_m_cafo -13772.4026269 722.3190727 -15833.923813
## dist_m_mine_well -16322.5110008 -2032.3464340 -4272.382880
## cvd_rate_adj 1289.5661935 135.9487143 343.936473
## res_rate_adj 1091.1856742 104.4979610 333.780710
## violent_crime_rate 104.4979610 40.1175363 160.725724
## property_crime_rate 333.7807097 160.7257236 1295.004010
## pct_less_hs 197.8827546 22.5579950 -3.138375
## pct_unemp 72.3576933 11.3130282 1.362247
## pct_limited_eng 104.0524036 12.7978322 -14.963510
## pct_hh_pov 201.6582659 29.1947400 64.236239
## pct_poc 297.8399442 46.4013012 -44.321973
## pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## mean_pm 1.1322329 0.1004399 0.4325162 0.7318245
## mean_o3 0.6373613 0.2885305 0.2956170 -0.6066485
## pct_tree_cover -7.5753471 -0.3330523 -2.8349116 0.3805472
## pct_impervious 56.8383947 25.9434246 41.9919053 82.2198624
## mean_aadt_intensity -4056.6889048 6003.3343312 2620.6197529 17850.1649192
## dist_m_tri -12372.1426191 -2527.2245090 -5408.8643368 -8842.7640785
## dist_m_npl -6760.5337115 2195.0514738 498.0033420 -1135.3843390
## dist_m_waste_site -11422.4985495 -1476.4094188 -4277.8133935 -7599.7432386
## dist_m_major_emit 8866.7491706 5212.7483023 9367.2843472 8682.2613524
## dist_m_cafo -26060.8337755 -1030.9691591 -7089.1582114 -855.3801591
## dist_m_mine_well -10037.6576614 -2827.2368665 -4814.6687400 -5030.4055237
## cvd_rate_adj 328.3044447 105.0153846 183.5853966 266.1004715
## res_rate_adj 197.8827546 72.3576933 104.0524036 201.6582659
## violent_crime_rate 22.5579950 11.3130282 12.7978322 29.1947400
## property_crime_rate -3.1383751 1.3622468 -14.9635105 64.2362387
## pct_less_hs 162.1681017 39.4206217 85.1910014 100.9072175
## pct_unemp 39.4206217 24.6546969 25.2172769 36.9693212
## pct_limited_eng 85.1910014 25.2172769 68.6532943 67.2758215
## pct_hh_pov 100.9072175 36.9693212 67.2758215 119.7157808
## pct_poc 238.8801445 72.7999599 142.1961838 155.4992975
## pct_poc
## mean_pm 1.632060
## mean_o3 1.202932
## pct_tree_cover -19.409179
## pct_impervious 88.356015
## mean_aadt_intensity 4526.271046
## dist_m_tri -18049.423325
## dist_m_npl -1456.894145
## dist_m_waste_site -8602.852068
## dist_m_major_emit 22698.243529
## dist_m_cafo -44526.371072
## dist_m_mine_well -24974.330302
## cvd_rate_adj 618.281729
## res_rate_adj 297.839944
## violent_crime_rate 46.401301
## property_crime_rate -44.321973
## pct_less_hs 238.880145
## pct_unemp 72.799960
## pct_limited_eng 142.196184
## pct_hh_pov 155.499297
## pct_poc 524.759104ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 pct_tree_cover pct_impervious mean_aadt_intensity
## [1,] 1.60876944 -0.2502907 -0.08261827 0.2084897 -0.02626143
## [2,] -1.40186806 0.6834152 0.32629926 0.5886571 0.04938980
## [3,] -0.03503482 0.2001460 3.50981981 -0.6665506 -0.15790801
## [4,] -1.28583023 0.6877893 0.18573791 0.3359288 -0.74617032
## [5,] -0.56482237 0.7133998 -0.93215008 -0.9301550 -1.15635722
## [6,] 0.25782234 -0.3023500 1.43693690 0.4015075 0.64126566
## dist_m_tri dist_m_npl dist_m_waste_site dist_m_major_emit dist_m_cafo
## [1,] -0.4008664 -1.44212141 -0.172775897 -0.1090638 -1.1354079
## [2,] -0.8894134 -0.08999604 -0.350992130 -1.4258114 2.0863310
## [3,] -0.1967327 -0.76363997 -0.007492447 -0.2805619 -0.1124210
## [4,] -0.1910117 0.43733697 1.597126043 0.4154599 0.7921355
## [5,] -0.3632728 -0.63324550 0.768623456 -0.4743524 -1.1310891
## [6,] -0.1913062 -0.71140077 -0.321936759 -0.9590895 1.0398621
## dist_m_mine_well cvd_rate_adj res_rate_adj violent_crime_rate
## [1,] -0.7748959 0.6917151 -0.2847192 0.2444833
## [2,] 1.8883051 0.7890362 1.8654606 -0.6194047
## [3,] 0.7160914 -0.5084805 -0.2265752 -0.8196807
## [4,] 0.1769998 -0.8884275 -0.6855261 -1.5754111
## [5,] -1.2592010 -1.1028189 -1.9428184 -1.1671633
## [6,] 1.1833114 -1.5425892 -1.3578439 -1.2303189
## property_crime_rate pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## [1,] -0.5008789 1.20091488 0.36793456 2.15383825 -0.3020187
## [2,] 0.3247153 -0.09436047 -0.96557105 0.02798425 0.2566428
## [3,] -0.2382061 -0.75386917 -1.03471894 -0.99792447 -0.8232412
## [4,] -0.9281724 -1.08099463 -0.82151747 -0.83491873 -0.5504902
## [5,] -0.9130100 -0.28055077 -0.89995692 -0.23668961 -1.2063898
## [6,] -0.2278392 -0.99332353 0.05987409 -0.37977738 0.9008223
## pct_poc
## [1,] 1.5727240
## [2,] -1.0419857
## [3,] -1.2081839
## [4,] -0.9439299
## [5,] 0.8424295
## [6,] -1.3629822Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 pct_tree_cover pct_impervious
## mean_pm 1.000000000 0.003172893 -0.105274276 0.06114033
## mean_o3 0.003172893 1.000000000 -0.043541201 -0.04109912
## pct_tree_cover -0.105274276 -0.043541201 1.000000000 0.14164056
## pct_impervious 0.061140333 -0.041099117 0.141640558 1.00000000
## mean_aadt_intensity -0.035493982 0.018889337 0.329716765 0.50844411
## dist_m_tri -0.159193706 0.056635532 -0.009161339 -0.44867872
## dist_m_npl -0.138426634 0.052836279 0.041781063 -0.17426369
## dist_m_waste_site -0.190232937 0.036984589 0.268331135 -0.15168685
## dist_m_major_emit 0.035715124 0.059253499 0.026770503 0.06211712
## dist_m_cafo -0.303095664 -0.001691929 0.479321466 0.18326720
## dist_m_mine_well -0.257510042 -0.058230361 0.477976199 0.02524829
## cvd_rate_adj 0.136954783 0.006789463 -0.176295758 0.38371166
## res_rate_adj 0.113962827 -0.001793836 -0.034307854 0.40251263
## violent_crime_rate 0.058730941 0.029772424 -0.205526308 0.31693831
## property_crime_rate 0.088879773 -0.025156291 -0.201827442 0.24673907
## pct_less_hs 0.142046220 0.016338825 -0.190810449 0.33564418
## pct_unemp 0.032317153 0.018969666 -0.021515177 0.39291400
## pct_limited_eng 0.083396591 0.011647067 -0.109746623 0.38111402
## pct_hh_pov 0.106858205 -0.018100029 0.011156172 0.56509450
## pct_poc 0.113823690 0.017142692 -0.271775006 0.29005220
## mean_aadt_intensity dist_m_tri dist_m_npl
## mean_pm -0.03549398 -0.159193706 -0.13842663
## mean_o3 0.01888934 0.056635532 0.05283628
## pct_tree_cover 0.32971677 -0.009161339 0.04178106
## pct_impervious 0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity 1.00000000 -0.062619247 0.06152095
## dist_m_tri -0.06261925 1.000000000 0.50138396
## dist_m_npl 0.06152095 0.501383960 1.00000000
## dist_m_waste_site 0.10755964 0.412369055 0.54385239
## dist_m_major_emit 0.09495686 0.175965418 0.65505772
## dist_m_cafo 0.27696155 0.196849357 0.23859436
## dist_m_mine_well 0.12008641 0.184760224 0.03659688
## cvd_rate_adj 0.05527416 -0.426652406 -0.20525615
## res_rate_adj 0.12199419 -0.376750794 -0.17601130
## violent_crime_rate 0.11041575 -0.062519618 -0.03185242
## property_crime_rate 0.07479259 -0.058223492 -0.15232247
## pct_less_hs -0.03883608 -0.379376300 -0.15916230
## pct_unemp 0.14739715 -0.198747643 0.13253691
## pct_limited_eng 0.03855846 -0.254907958 0.01801953
## pct_hh_pov 0.19888999 -0.315587892 -0.03111065
## pct_poc 0.02408835 -0.307674381 -0.01906733
## dist_m_waste_site dist_m_major_emit dist_m_cafo
## mean_pm -0.19023294 0.03571512 -0.303095664
## mean_o3 0.03698459 0.05925350 -0.001691929
## pct_tree_cover 0.26833114 0.02677050 0.479321466
## pct_impervious -0.15168685 0.06211712 0.183267205
## mean_aadt_intensity 0.10755964 0.09495686 0.276961553
## dist_m_tri 0.41236906 0.17596542 0.196849357
## dist_m_npl 0.54385239 0.65505772 0.238594356
## dist_m_waste_site 1.00000000 0.18977973 0.355027509
## dist_m_major_emit 0.18977973 1.00000000 -0.138307324
## dist_m_cafo 0.35502751 -0.13830732 1.000000000
## dist_m_mine_well 0.28275484 -0.27042332 0.652378929
## cvd_rate_adj -0.41298787 0.11328659 -0.151743889
## res_rate_adj -0.42432287 -0.01256670 -0.061257230
## violent_crime_rate -0.25287368 -0.01789622 0.016755559
## property_crime_rate -0.26866460 -0.20976678 -0.064647236
## pct_less_hs -0.38800832 0.21893159 -0.300678627
## pct_unemp -0.12862329 0.33009857 -0.030506530
## pct_limited_eng -0.22333346 0.35547555 -0.125707430
## pct_hh_pov -0.30045944 0.24950766 -0.011486308
## pct_poc -0.16245202 0.31155805 -0.285584268
## dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.25751004 0.136954783 0.113962827
## mean_o3 -0.05823036 0.006789463 -0.001793836
## pct_tree_cover 0.47797620 -0.176295758 -0.034307854
## pct_impervious 0.02524829 0.383711656 0.402512635
## mean_aadt_intensity 0.12008641 0.055274160 0.121994187
## dist_m_tri 0.18476022 -0.426652406 -0.376750794
## dist_m_npl 0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site 0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit -0.27042332 0.113286594 -0.012566704
## dist_m_cafo 0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well 1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj -0.41075254 1.000000000 0.864359590
## res_rate_adj -0.23476565 0.864359590 1.000000000
## violent_crime_rate -0.15245003 0.475234675 0.499449246
## property_crime_rate -0.05640681 0.211613232 0.280786581
## pct_less_hs -0.37449548 0.570813439 0.470409304
## pct_unemp -0.27052616 0.468277441 0.441149256
## pct_limited_eng -0.27607853 0.490577454 0.380164971
## pct_hh_pov -0.21843600 0.538480631 0.557944498
## pct_poc -0.51797735 0.597594464 0.393598671
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.05873094 0.088879773 0.14204622
## mean_o3 0.02977242 -0.025156291 0.01633882
## pct_tree_cover -0.20552631 -0.201827442 -0.19081045
## pct_impervious 0.31693831 0.246739067 0.33564418
## mean_aadt_intensity 0.11041575 0.074792588 -0.03883608
## dist_m_tri -0.06251962 -0.058223492 -0.37937630
## dist_m_npl -0.03185242 -0.152322474 -0.15916230
## dist_m_waste_site -0.25287368 -0.268664603 -0.38800832
## dist_m_major_emit -0.01789622 -0.209766780 0.21893159
## dist_m_cafo 0.01675556 -0.064647236 -0.30067863
## dist_m_mine_well -0.15245003 -0.056406808 -0.37449548
## cvd_rate_adj 0.47523468 0.211613232 0.57081344
## res_rate_adj 0.49944925 0.280786581 0.47040930
## violent_crime_rate 1.00000000 0.705151942 0.27967307
## property_crime_rate 0.70515194 1.000000000 -0.00684836
## pct_less_hs 0.27967307 -0.006848360 1.00000000
## pct_unemp 0.35971778 0.007623781 0.62343462
## pct_limited_eng 0.24385889 -0.050184228 0.80738433
## pct_hh_pov 0.42127121 0.163143151 0.72420883
## pct_poc 0.31980337 -0.053765481 0.81887450
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.032317153 0.08339659 0.10685820 0.11382369
## mean_o3 0.018969666 0.01164707 -0.01810003 0.01714269
## pct_tree_cover -0.021515177 -0.10974662 0.01115617 -0.27177501
## pct_impervious 0.392914001 0.38111402 0.56509450 0.29005220
## mean_aadt_intensity 0.147397153 0.03855846 0.19888999 0.02408835
## dist_m_tri -0.198747643 -0.25490796 -0.31558789 -0.30767438
## dist_m_npl 0.132536906 0.01801953 -0.03111065 -0.01906733
## dist_m_waste_site -0.128623290 -0.22333346 -0.30045944 -0.16245202
## dist_m_major_emit 0.330098571 0.35547555 0.24950766 0.31155805
## dist_m_cafo -0.030506530 -0.12570743 -0.01148631 -0.28558427
## dist_m_mine_well -0.270526163 -0.27607853 -0.21843600 -0.51797735
## cvd_rate_adj 0.468277441 0.49057745 0.53848063 0.59759446
## res_rate_adj 0.441149256 0.38016497 0.55794450 0.39359867
## violent_crime_rate 0.359717785 0.24385889 0.42127121 0.31980337
## property_crime_rate 0.007623781 -0.05018423 0.16314315 -0.05376548
## pct_less_hs 0.623434625 0.80738433 0.72420883 0.81887450
## pct_unemp 1.000000000 0.61293958 0.68048090 0.64003145
## pct_limited_eng 0.612939575 1.00000000 0.74208323 0.74916462
## pct_hh_pov 0.680480902 0.74208323 1.00000000 0.62040136
## pct_poc 0.640031449 0.74916462 0.62040136 1.00000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
NOTE: It’ll be interesting to see what comes out of our BEAMERS discussion re: adjusting for gestational age. It’s currently in the analysis
There are four continuous covariates; all of the others have been coded as dummy variables. For the dummy variables, the reference groups are: white_re, ed_grad, norm_bmi
W <- select(hs_data2,
lat, lon, lat_lon_int,
latina_re, black_re, other_re,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w) %>%
as.matrix()
head(W)## lat lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133 -4170.944 1 0 0 0 0
## [2,] 39.62671 -104.9927 -4160.517 0 0 1 0 0
## [3,] 39.74934 -104.9129 -4170.219 0 0 0 0 0
## [4,] 39.68397 -104.8933 -4162.583 0 0 0 0 0
## [5,] 39.79134 -104.7669 -4168.814 0 1 0 0 0
## [6,] 39.68050 -104.9451 -4164.274 1 0 0 0 0
## ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,] 1 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 1 0
## [5,] 0 1 0 0 0 1 0
## [6,] 1 0 0 0 0 0 0
## concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,] 0 0 0 0 0 19
## [2,] 0 1 0 0 0 36
## [3,] 0 1 0 0 0 34
## [4,] 0 1 0 0 0 28
## [5,] 0 1 0 0 0 30
## [6,] 0 1 0 0 0 22
## any_smoker smokeSH mean_cpss mean_epsd male gest_age_w
## [1,] 0 1 29 0 0 40.57143
## [2,] 0 0 19 2 1 35.85714
## [3,] 0 0 19 1 0 40.42857
## [4,] 0 0 20 0 0 36.28571
## [5,] 0 0 15 0 1 38.42857
## [6,] 0 0 17 1 0 40.71429Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "gest_age_w"W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:20], W.s[,4],
W[,22:23], W.s[,5:6],
W[,26], W.s[,7])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "" ""colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,] 0.9587536 0.5410850 -0.5821980 1 0 0 0
## [2,] -1.5498523 -1.6236392 0.6519093 0 0 1 0
## [3,] 0.2887793 -0.6606299 -0.4964164 0 0 0 0
## [4,] -0.6913627 -0.4239607 0.4073829 0 0 0 0
## [5,] 0.9185421 1.1019032 -0.3300513 0 1 0 0
## [6,] -0.7433125 -1.0489343 0.2071583 1 0 0 0
## ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,] 0 1 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 0 0 1 0
## [5,] 0 0 1 0 0 0 1 0
## [6,] 0 1 0 0 0 0 0 0
## concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,] 0 0 0 0 0 -1.39815187
## [2,] 0 1 0 0 0 1.35109608
## [3,] 0 1 0 0 0 1.02765515
## [4,] 0 1 0 0 0 0.05733234
## [5,] 0 1 0 0 0 0.38077328
## [6,] 0 1 0 0 0 -0.91299047
## any_smoker smokeSH mean_cpss mean_epsd male gest_age_w
## [1,] 0 1 3.3147856 -1.2832098 0 0.7037686
## [2,] 0 0 0.1179652 -0.6860171 1 -1.9146645
## [3,] 0 0 0.1179652 -0.9846134 0 0.6244221
## [4,] 0 0 0.4376472 -1.2832098 0 -1.6766251
## [5,] 0 0 -1.1607630 -1.2832098 1 -0.4864283
## [6,] 0 0 -0.5213989 -0.9846134 0 0.7831150summary(W.scaled)## lat lon lat_lon_int latina_re
## Min. :-2.45418 Min. :-2.5043 Min. :-3.48430 Min. :0.0000
## 1st Qu.:-0.62577 1st Qu.:-0.5848 1st Qu.:-0.48738 1st Qu.:0.0000
## Median : 0.03151 Median : 0.1214 Median : 0.02121 Median :0.0000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000 Mean :0.2653
## 3rd Qu.: 0.42402 3rd Qu.: 0.6654 3rd Qu.: 0.60627 3rd Qu.:1.0000
## Max. : 4.00304 Max. : 4.5531 Max. : 2.60273 Max. :1.0000
## black_re other_re ed_no_hs ed_hs
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.1717 Mean :0.06689 Mean :0.1527 Mean :0.1851
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## ed_aa ed_4yr low_bmi ovwt_bmi
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.000
## Mean :0.2319 Mean :0.2185 Mean :0.03344 Mean :0.262
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:1.000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.000
## obese_bmi concep_spring concep_summer concep_fall
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1996 Mean :0.2497 Mean :0.2408 Mean :0.2709
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_2010 concep_2011 concep_2012 concep_2013
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1616 Mean :0.3021 Mean :0.2932 Mean :0.2419
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## maternal_age any_smoker smokeSH mean_cpss
## Min. :-1.88331 Min. :0.00000 Min. :0.0000 Min. :-5.9560
## 1st Qu.:-0.91299 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:-0.5214
## Median : 0.05733 Median :0.00000 Median :0.0000 Median : 0.0114
## Mean : 0.00000 Mean :0.08696 Mean :0.2575 Mean : 0.0000
## 3rd Qu.: 0.70421 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.: 0.5442
## Max. : 2.64486 Max. :1.00000 Max. :1.0000 Max. : 4.5935
## mean_epsd male gest_age_w
## Min. :-1.2832 Min. :0.0000 Min. :-7.7070
## 1st Qu.:-0.7855 1st Qu.:0.0000 1st Qu.:-0.3277
## Median :-0.1884 Median :1.0000 Median : 0.1483
## Mean : 0.0000 Mean :0.5117 Mean : 0.0000
## 3rd Qu.: 0.6079 3rd Qu.:1.0000 3rd Qu.: 0.6244
## Max. : 6.0324 Max. :1.0000 Max. : 2.9255Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int latina_re
## lat 1.0000000000 -0.25261855699 -0.9261702843 0.02075377736
## lon -0.2526185570 1.00000000000 0.5988415501 0.01061991294
## lat_lon_int -0.9261702843 0.59884155012 1.0000000000 -0.01302007756
## latina_re 0.0207537774 0.01061991294 -0.0130200776 0.19514701784
## black_re -0.0122649034 0.04784916212 0.0288174353 -0.04560340022
## other_re -0.0009403195 -0.00123694771 0.0002902002 -0.01776755853
## ed_no_hs 0.0058668471 0.01732912905 0.0019047436 0.03978788422
## ed_hs -0.0130652792 0.04117136599 0.0268694085 0.02896808807
## ed_aa -0.0071789427 0.04676104709 0.0241824221 0.01318258282
## ed_4yr 0.0022352364 -0.00766878563 -0.0048607788 -0.03571926262
## low_bmi -0.0029774584 -0.00003551643 0.0024531145 0.00004479216
## ovwt_bmi 0.0205880066 0.00512460048 -0.0150602639 0.02081218148
## obese_bmi 0.0165669344 0.00976713009 -0.0098964732 0.02065416468
## concep_spring 0.0143292896 -0.00046075172 -0.0120393632 -0.00606436136
## concep_summer -0.0140319053 -0.00711327850 0.0088444045 -0.00481142499
## concep_fall 0.0054905592 0.01642183233 0.0018457750 0.01732710225
## concep_2010 0.0110681241 0.00844610317 -0.0058861055 -0.00610790930
## concep_2011 -0.0220635440 0.01869831001 0.0255410960 -0.00882156792
## concep_2012 0.0024435961 -0.00706763788 -0.0047707939 0.01252065416
## concep_2013 0.0074817863 -0.02068066481 -0.0142344221 0.00158887761
## maternal_age 0.0307789398 -0.17980907079 -0.0955945618 -0.10858833047
## any_smoker -0.0082274331 0.02279799333 0.0156963705 -0.00858889752
## smokeSH -0.0111042258 0.04668855425 0.0273846128 -0.00590510033
## mean_cpss -0.0258360855 -0.01114736129 0.0170462313 -0.04668314421
## mean_epsd -0.0347375477 0.05084465609 0.0485855489 0.04322362524
## male 0.0290047629 -0.02552947737 -0.0339519192 -0.00087717989
## gest_age_w 0.0111191604 -0.03926647196 -0.0245324539 -0.02639363168
## black_re other_re ed_no_hs ed_hs
## lat -0.0122649034 -0.0009403195 0.0058668471 -0.01306527915
## lon 0.0478491621 -0.0012369477 0.0173291290 0.04117136599
## lat_lon_int 0.0288174353 0.0002902002 0.0019047436 0.02686940852
## latina_re -0.0456034002 -0.0177675585 0.0397878842 0.02896808807
## black_re 0.1423669175 -0.0114966555 0.0128118032 0.01506758640
## other_re -0.0114966555 0.0624850693 -0.0035311156 0.00658071548
## ed_no_hs 0.0128118032 -0.0035311156 0.1295488931 -0.02829620561
## ed_hs 0.0150675864 0.0065807155 -0.0282962056 0.15098194378
## ed_aa 0.0192967133 0.0023291925 -0.0354554865 -0.04296066253
## ed_4yr -0.0163503842 -0.0034713927 -0.0334099777 -0.04048216276
## low_bmi 0.0020641722 -0.0011235368 -0.0039977007 -0.00173196369
## ovwt_bmi -0.0003857103 -0.0052668120 0.0045849757 -0.00612657270
## obese_bmi 0.0069962872 0.0022620043 0.0063181836 0.02441297380
## concep_spring 0.0017220099 0.0044829491 -0.0002364031 0.00395788541
## concep_summer -0.0079058170 0.0017319637 -0.0044530877 -0.00331835284
## concep_fall -0.0063828834 -0.0047479694 0.0110338032 0.00226573698
## concep_2010 0.0090467730 -0.0007801302 -0.0001629937 0.00576574693
## concep_2011 0.0183859392 -0.0023739847 0.0096091635 -0.00463350056
## concep_2012 -0.0146793876 0.0004553870 -0.0035360925 0.00371526119
## concep_2013 -0.0125617136 0.0027733815 -0.0057396182 -0.00464096592
## maternal_age -0.0895968722 -0.0133074822 -0.1376124653 -0.10868310364
## any_smoker 0.0185364907 -0.0013586957 0.0179541925 0.00174689441
## smokeSH 0.0349789477 0.0084246596 0.0309364548 0.02483352246
## mean_cpss -0.0233123370 0.0255604593 -0.0561153540 -0.03433895561
## mean_epsd 0.0220578552 0.0202679881 0.0670107276 0.02014619096
## male 0.0002202281 0.0003322086 -0.0135085702 0.00006345557
## gest_age_w -0.0368471269 -0.0054750903 -0.0076928484 -0.01723767893
## ed_aa ed_4yr low_bmi ovwt_bmi
## lat -0.007178943 0.0022352364 -0.00297745845 0.0205880066
## lon 0.046761047 -0.0076687856 -0.00003551643 0.0051246005
## lat_lon_int 0.024182422 -0.0048607788 0.00245311454 -0.0150602639
## latina_re 0.013182583 -0.0357192626 0.00004479216 0.0208121815
## black_re 0.019296713 -0.0163503842 0.00206417224 -0.0003857103
## other_re 0.002329193 -0.0034713927 -0.00112353679 -0.0052668120
## ed_no_hs -0.035455487 -0.0334099777 -0.00399770067 0.0045849757
## ed_hs -0.042960663 -0.0404821628 -0.00173196369 -0.0061265727
## ed_aa 0.178312629 -0.0507246377 0.00786102484 0.0150750518
## ed_4yr -0.050724638 0.1709517837 -0.00173569637 0.0040748427
## low_bmi 0.007861025 -0.0017356964 0.03236233875 -0.0087717989
## ovwt_bmi 0.015075052 0.0040748427 -0.00877179885 0.1935643614
## obese_bmi 0.009478520 -0.0124024526 -0.00668149785 -0.0523383998
## concep_spring 0.006761128 -0.0066354615 -0.00501298973 0.0092806876
## concep_summer -0.011257764 0.0064762004 0.00309812470 -0.0051212375
## concep_fall -0.007084627 0.0010078237 0.00320637243 0.0026091436
## concep_2010 0.004884834 0.0003533604 0.00128404204 -0.0033345278
## concep_2011 0.002410067 0.0053402214 0.00439336479 0.0055828456
## concep_2012 -0.005564182 -0.0061016882 -0.00535266364 -0.0043547938
## concep_2013 -0.002587992 0.0006519748 -0.00028741639 0.0023988692
## maternal_age -0.040296710 0.1091044519 -0.01089529356 0.0089002276
## any_smoker 0.011063665 -0.0156735248 0.00155279503 -0.0060656056
## smokeSH 0.022806677 -0.0362443263 0.00142215122 -0.0106232083
## mean_cpss 0.030714793 0.0282429323 0.00484169668 -0.0082476896
## mean_epsd 0.025424770 -0.0463684315 0.00946748435 -0.0019127169
## male 0.000630823 0.0063679527 -0.00262407430 0.0008361204
## gest_age_w -0.035168407 0.0301476493 -0.00601412877 -0.0148466585
## obese_bmi concep_spring concep_summer concep_fall
## lat 0.0165669344 0.0143292896 -0.01403190526 0.0054905592
## lon 0.0097671301 -0.0004607517 -0.00711327850 0.0164218323
## lat_lon_int -0.0098964732 -0.0120393632 0.00884440451 0.0018457750
## latina_re 0.0206541647 -0.0060643614 -0.00481142499 0.0173271022
## black_re 0.0069962872 0.0017220099 -0.00790581701 -0.0063828834
## other_re 0.0022620043 0.0044829491 0.00173196369 -0.0047479694
## ed_no_hs 0.0063181836 -0.0002364031 -0.00445308767 0.0110338032
## ed_hs 0.0244129738 0.0039578854 -0.00331835284 0.0022657370
## ed_aa 0.0094785197 0.0067611284 -0.01125776398 -0.0070846273
## ed_4yr -0.0124024526 -0.0066354615 0.00647620043 0.0010078237
## low_bmi -0.0066814978 -0.0050129897 0.00309812470 0.0032063724
## ovwt_bmi -0.0523383998 0.0092806876 -0.00512123746 0.0026091436
## obese_bmi 0.1599105152 -0.0085938744 -0.00346392738 0.0005673674
## concep_spring -0.0085938744 0.1875696767 -0.06020066890 -0.0677257525
## concep_summer -0.0034639274 -0.0602006689 0.18302078356 -0.0653069756
## concep_fall 0.0005673674 -0.0677257525 -0.06530697563 0.1977350096
## concep_2010 -0.0043921206 -0.0236714146 0.00009331701 0.0287043120
## concep_2011 0.0032598742 0.0003633142 -0.00140348782 -0.0127396381
## concep_2012 0.0072737498 -0.0085677457 0.00186260750 0.0019559245
## concep_2013 -0.0059187868 0.0321545529 -0.00028368371 -0.0176182513
## maternal_age 0.0027900741 -0.0149065532 0.01490413862 -0.0196470231
## any_smoker 0.0027173913 0.0016983696 0.00024262422 -0.0023777174
## smokeSH 0.0110524666 -0.0041134138 -0.00627836837 -0.0028778966
## mean_cpss -0.0087226114 0.0079650833 0.01166899615 -0.0055888831
## mean_epsd 0.0281330380 -0.0063209443 -0.01563660013 0.0265650931
## male -0.0017804885 -0.0062746357 -0.00393797778 0.0018476768
## gest_age_w -0.0214614301 -0.0179961830 0.01920131892 0.0141959621
## concep_2010 concep_2011 concep_2012 concep_2013
## lat 0.01106812411 -0.0220635440 0.002443596 0.0074817863
## lon 0.00844610317 0.0186983100 -0.007067638 -0.0206806648
## lat_lon_int -0.00588610547 0.0255410960 -0.004770794 -0.0142344221
## latina_re -0.00610790930 -0.0088215679 0.012520654 0.0015888776
## black_re 0.00904677297 0.0183859392 -0.014679388 -0.0125617136
## other_re -0.00078013020 -0.0023739847 0.000455387 0.0027733815
## ed_no_hs -0.00016299371 0.0096091635 -0.003536093 -0.0057396182
## ed_hs 0.00576574693 -0.0046335006 0.003715261 -0.0046409659
## ed_aa 0.00488483437 0.0024100673 -0.005564182 -0.0025879917
## ed_4yr 0.00035336041 0.0053402214 -0.006101688 0.0006519748
## low_bmi 0.00128404204 0.0043933648 -0.005352664 -0.0002874164
## ovwt_bmi -0.00333452779 0.0055828456 -0.004354794 0.0023988692
## obese_bmi -0.00439212056 0.0032598742 0.007273750 -0.0059187868
## concep_spring -0.02367141464 0.0003633142 -0.008567746 0.0321545529
## concep_summer 0.00009331701 -0.0014034878 0.001862608 -0.0002836837
## concep_fall 0.02870431199 -0.0127396381 0.001955925 -0.0176182513
## concep_2010 0.13567048893 -0.0488918916 -0.047448589 -0.0391495959
## concep_2011 -0.04889189162 0.2110780976 -0.088679776 -0.0731692447
## concep_2012 -0.04744858855 -0.0886797758 0.207464863 -0.0710092670
## concep_2013 -0.03914959588 -0.0731692447 -0.071009267 0.1835981048
## maternal_age -0.02663971411 -0.0380704459 0.031448396 0.0348222009
## any_smoker 0.00266886646 0.0105298913 -0.011015140 -0.0020865683
## smokeSH 0.00631569517 0.0136280160 -0.018670867 -0.0021014990
## mean_cpss 0.00832724099 -0.0113573536 -0.011161856 0.0104924310
## mean_epsd -0.01748485806 0.0347867417 -0.022850868 0.0069811381
## male 0.00089584329 -0.0029824116 -0.001761825 0.0044194935
## gest_age_w 0.01072301448 -0.0118973482 -0.026416733 0.0268056111
## maternal_age any_smoker smokeSH mean_cpss mean_epsd
## lat 0.030778940 -0.0082274331 -0.011104226 -0.025836085 -0.034737548
## lon -0.179809071 0.0227979933 0.046688554 -0.011147361 0.050844656
## lat_lon_int -0.095594562 0.0156963705 0.027384613 0.017046231 0.048585549
## latina_re -0.108588330 -0.0085888975 -0.005905100 -0.046683144 0.043223625
## black_re -0.089596872 0.0185364907 0.034978948 -0.023312337 0.022057855
## other_re -0.013307482 -0.0013586957 0.008424660 0.025560459 0.020267988
## ed_no_hs -0.137612465 0.0179541925 0.030936455 -0.056115354 0.067010728
## ed_hs -0.108683104 0.0017468944 0.024833522 -0.034338956 0.020146191
## ed_aa -0.040296710 0.0110636646 0.022806677 0.030714793 0.025424770
## ed_4yr 0.109104452 -0.0156735248 -0.036244326 0.028242932 -0.046368432
## low_bmi -0.010895294 0.0015527950 0.001422151 0.004841697 0.009467484
## ovwt_bmi 0.008900228 -0.0060656056 -0.010623208 -0.008247690 -0.001912717
## obese_bmi 0.002790074 0.0027173913 0.011052467 -0.008722611 0.028133038
## concep_spring -0.014906553 0.0016983696 -0.004113414 0.007965083 -0.006320944
## concep_summer 0.014904139 0.0002426242 -0.006278368 0.011668996 -0.015636600
## concep_fall -0.019647023 -0.0023777174 -0.002877897 -0.005588883 0.026565093
## concep_2010 -0.026639714 0.0026688665 0.006315695 0.008327241 -0.017484858
## concep_2011 -0.038070446 0.0105298913 0.013628016 -0.011357354 0.034786742
## concep_2012 0.031448396 -0.0110151398 -0.018670867 -0.011161856 -0.022850868
## concep_2013 0.034822201 -0.0020865683 -0.002101499 0.010492431 0.006981138
## maternal_age 1.000000000 -0.0466296108 -0.155964054 0.100637638 -0.160410684
## any_smoker -0.046629611 0.0794836957 0.049010093 0.017642908 0.042144665
## smokeSH -0.155964054 0.0490100932 0.191419314 0.031721118 0.108180210
## mean_cpss 0.100637638 0.0176429080 0.031721118 1.000000000 0.455187203
## mean_epsd -0.160410684 0.0421446647 0.108180210 0.455187203 1.000000000
## male 0.023413804 0.0023291925 0.002004449 -0.003315304 0.001541815
## gest_age_w 0.091663607 -0.0149814181 -0.050311537 -0.037142336 -0.137187808
## male gest_age_w
## lat 0.02900476291 0.011119160
## lon -0.02552947737 -0.039266472
## lat_lon_int -0.03395191918 -0.024532454
## latina_re -0.00087717989 -0.026393632
## black_re 0.00022022814 -0.036847127
## other_re 0.00033220855 -0.005475090
## ed_no_hs -0.01350857023 -0.007692848
## ed_hs 0.00006345557 -0.017237679
## ed_aa 0.00063082298 -0.035168407
## ed_4yr 0.00636795270 0.030147649
## low_bmi -0.00262407430 -0.006014129
## ovwt_bmi 0.00083612040 -0.014846658
## obese_bmi -0.00178048853 -0.021461430
## concep_spring -0.00627463569 -0.017996183
## concep_summer -0.00393797778 0.019201319
## concep_fall 0.00184767678 0.014195962
## concep_2010 0.00089584329 0.010723014
## concep_2011 -0.00298241161 -0.011897348
## concep_2012 -0.00176182513 -0.026416733
## concep_2013 0.00441949355 0.026805611
## maternal_age 0.02341380415 0.091663607
## any_smoker 0.00232919255 -0.014981418
## smokeSH 0.00200444935 -0.050311537
## mean_cpss -0.00331530432 -0.037142336
## mean_epsd 0.00154181454 -0.137187808
## male 0.25014184185 -0.007427180
## gest_age_w -0.00742717951 1.000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.4 Response data: birth weight (in grams)
Y <- select(hs_data2, birth_weight) %>%
as.matrix()
head(Y)## birth_weight
## [1,] 2860
## [2,] 2755
## [3,] 3505
## [4,] 2695
## [5,] 3355
## [6,] 3810Distribution of birth weight and scaled birth weight
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
1.5 Scatterplots of exposures and outcome (birth weight)
Both birth weight (Y) and the exposures are scaled here
NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori
df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
lm.x <- lm(birth_weight ~ df[,x], data = df)
plot(df[,c(x, 1)],
xlab = paste0(colnames(df)[x], " beta: ",
round(summary(lm.x)$coef[2,1],4),
"; p = ",
round(summary(lm.x)$coef[2,4],4)))
abline(lm.x)
})
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## NULL2 Is gestational age a potenital mediator?
I.e., is there a relationship between our exposures and gestational age?
The DAG might look something like this:
exposures —> gestational age —> birth weight _________________________________^
2.1 Scatter plots for exposures and gestational age
Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery
Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.
df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
plot(df2[,c(x, 1)],
xlab = paste0(colnames(df2)[x], " beta: ",
round(summary(lm.x)$coef[2,1],4),
"; p = ",
round(summary(lm.x)$coef[2,4],4)))
abline(lm.x)
})
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## NULLDropping gest_age_w from the covariates
W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"3 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 630.9573#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(bw_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 20 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(bw_ridge)## 21 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 3764.2974431484
## mean_pm 7.7753350262
## mean_o3 -8.5947719688
## pct_tree_cover -0.0074346757
## pct_impervious -0.4874093432
## mean_aadt_intensity -0.0003363759
## dist_m_tri -0.0005811201
## dist_m_npl 0.0002060546
## dist_m_waste_site 0.0021158752
## dist_m_major_emit -0.0002875616
## dist_m_cafo -0.0003386587
## dist_m_mine_well -0.0032347267
## cvd_rate_adj -0.1632413722
## res_rate_adj -0.1502653198
## violent_crime_rate -0.3428576912
## property_crime_rate -0.0247667418
## pct_less_hs -0.7383109357
## pct_unemp -4.4184536971
## pct_limited_eng -0.4337403128
## pct_hh_pov -0.4325335405
## pct_poc -0.5119074150Ridge regression predictions
ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.
4 Nonparametric Bayesian Shrinkage (NPB): Birth weight
Still, we wanted to try to fit the NPB model with these data.
4.1 Finding the NPB priors
Start with Lauren’s from the example in the vignette
In an email from April 29, Lauren provided me with some additional guidance on finding the NPB priors:
- Keep alpha.pi and beta.pi set to 1, and then let a.phi1 take values 1, 10, and 100 and see how the results change.
- Keep a.phi1 set to 1 (or 10 or 100), and mess with alpha.pi and beta.pi.
- Run the following code: alpha.pi=1 beta.pi=1 plot(density(rbeta(10000, alpha.pi, beta.pi))) and then change alpha.pi and beta.pi and see how it changes the prior distribution.
- This is the distribution of the probability of a main effect regression coefficient being 0 (aka exclusion probability). We don’t want this to be too informative (you don’t want high mass around just a few values). Also alpha.pi and beta.pi don’t have to be the same value. You might try alpha.pi = 1 and beta.pi = 2 to get a slightly lower prior probability of exclusion. Try not to change all three (alpha.pi, beta.pi, and a.phi1) at once.
- When playing with the priors, set “interact=FALSE” and just fit the modelwith the main effects. Most of the interactions were null anyway so it shouldn’t change the results too much and it will make the code run a lot faster. Then when you find a set of priors you like, you can add in “interact=TRUE” and “XWinteract=TRUE.”
Some additional feedback from Lauren during our 6/10 meeting:
- The confidence intervals were really wide and heavily skewed. I’m going to try adjusting the sig2inv.mu1 parameter after the a.phi1 parameter to see if this helps
- the rbeta distributions is interpreted as the exclusion probability, so I should try to aim to have most of the mass of that distribution in the middle, since we hypothesize that maybe 40-60% of the predictors will be important. The way to do this is to set alpha.pi and beta.pi to the same value
- I should set the burn in number to be about half the iterations
Note: I’m including far fewer iterations of the priors than in the previous version of the document.
4.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.127441460 2.6609141 0.000000 0 0.026
## [2,] -0.963719549 8.8753281 -1.526898 0 0.034
## [3,] 0.029752904 1.6712101 0.000000 0 0.016
## [4,] -0.055071939 0.6099851 0.000000 0 0.012
## [5,] 0.169061015 2.5847844 0.000000 0 0.008
## [6,] 0.053765120 2.4427873 0.000000 0 0.010
## [7,] 0.141469800 2.3645803 0.000000 0 0.024
## [8,] 0.462321176 4.3762285 0.000000 0 0.034
## [9,] -0.001465069 1.4819965 0.000000 0 0.016
## [10,] -0.118832429 3.3222775 0.000000 0 0.020
## [11,] -0.160301912 2.5767658 0.000000 0 0.024
## [12,] -0.072292473 1.7048618 0.000000 0 0.018
## [13,] -0.105399537 2.0370932 0.000000 0 0.018
## [14,] -0.073266119 2.0667136 0.000000 0 0.018
## [15,] -0.027547929 0.8532218 0.000000 0 0.020
## [16,] 0.008342958 1.8775514 0.000000 0 0.018
## [17,] -0.606745402 4.5618241 -3.743610 0 0.032
## [18,] -0.009390117 1.4188808 0.000000 0 0.014
## [19,] -0.028581985 0.8229871 0.000000 0 0.014
## [20,] -0.120797095 1.2799276 0.000000 0 0.026plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
4.1.2 Adjust alpha.pi and beta.pi
For now, leave a.phi1 and sig2inv.mu1 alone for now.
alpha.pi and beta.pi are responisble for the exclusion probability distribution. If we thing we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value
4.1.2.1 Try making alpha.pi and beta.pi 2
plot(density(rbeta(10000, 2, 2)))
priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.031460972 2.759754 0.0000000 0.00000 0.036
## [2,] -1.106775179 8.286496 -9.3607570 0.00000 0.048
## [3,] -0.071148608 1.803463 0.0000000 0.00000 0.030
## [4,] -0.212002282 1.877947 0.0000000 0.00000 0.032
## [5,] 0.103107143 2.919152 0.0000000 0.00000 0.024
## [6,] -0.017910531 2.646031 -1.6968561 0.00000 0.040
## [7,] -0.023801697 1.266272 0.0000000 0.00000 0.030
## [8,] 1.038432554 6.790843 0.0000000 19.33131 0.056
## [9,] 0.047453723 1.878220 0.0000000 0.00000 0.028
## [10,] -0.479271478 7.450079 -5.9197197 0.00000 0.046
## [11,] -0.436139635 3.614531 -5.5220092 0.00000 0.058
## [12,] -0.222781424 2.613901 -4.1434755 0.00000 0.040
## [13,] -0.423866505 3.383142 -4.6391150 0.00000 0.052
## [14,] -0.028696447 1.399109 0.0000000 0.00000 0.028
## [15,] -0.385945760 2.788175 -4.6318980 0.00000 0.046
## [16,] -0.328050395 2.710702 -4.3542325 0.00000 0.050
## [17,] -1.713017799 7.939331 -28.1312295 0.00000 0.092
## [18,] -0.190778711 1.671843 -0.7519376 0.00000 0.038
## [19,] -0.333680654 2.854248 -4.4999921 0.00000 0.058
## [20,] 0.004390389 4.393540 0.0000000 0.00000 0.030plot(fit.npb.12$beta[,1], type = "l")
plot(fit.npb.12$beta[,2], type = "l")
plot(fit.npb.12$beta[,13], type = "l")
4.1.2.2 Try making alpha.pi and beta.pi 5
plot(density(rbeta(10000, 5, 5)))
priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.42988258 5.099271 -12.173939 7.3648286 0.218
## [2,] -2.15655907 8.493732 -29.545431 5.5182644 0.252
## [3,] -0.37768748 4.028902 -9.478056 6.3596266 0.182
## [4,] -1.06819301 4.527702 -14.067572 3.9656823 0.208
## [5,] -0.05635313 4.033547 -7.708414 7.8425320 0.198
## [6,] -0.35015332 4.694971 -10.378587 7.3842082 0.240
## [7,] 0.01706464 3.583146 -7.870653 7.9917422 0.188
## [8,] 1.89609039 10.160326 -7.972503 27.9486549 0.258
## [9,] -0.09853021 4.475731 -8.469732 7.2192917 0.198
## [10,] -0.75705052 8.136366 -17.109856 18.2214526 0.300
## [11,] -1.95553682 7.597143 -18.455183 5.7648459 0.274
## [12,] -1.00933065 5.070416 -15.617421 5.7672188 0.234
## [13,] -2.07989371 7.125055 -22.524249 2.5222388 0.228
## [14,] -0.57502090 3.454515 -9.412140 5.2100416 0.202
## [15,] -1.55139794 5.453769 -15.555001 3.9013770 0.238
## [16,] -1.24221196 5.027768 -16.604305 0.2111787 0.208
## [17,] -3.69262176 9.960522 -37.080086 0.2158329 0.306
## [18,] -1.08529982 4.555619 -11.956445 2.3442693 0.214
## [19,] -1.23624033 5.294009 -13.787500 4.2793005 0.222
## [20,] -0.66889158 5.208466 -14.717921 6.8705824 0.202plot(fit.npb.13$beta[,1], type = "l")
plot(fit.npb.13$beta[,2], type = "l")
plot(fit.npb.13$beta[,13], type = "l")
4.1.2.3 Try making alpha.pi and beta.pi 8
plot(density(rbeta(10000, 8, 8)))
priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.21728605 4.841955 -10.179889 12.293195 0.294
## [2,] -3.25577064 10.082421 -35.532776 6.413138 0.424
## [3,] -0.06555033 5.603873 -10.942005 14.865837 0.356
## [4,] -0.91170821 5.266306 -12.338381 5.540108 0.304
## [5,] 0.01164678 4.372853 -8.999654 13.182631 0.316
## [6,] 0.18146622 5.109335 -10.637517 12.154360 0.326
## [7,] 0.37243590 5.087502 -9.224864 14.704406 0.328
## [8,] 1.82211841 7.556446 -6.276737 23.661811 0.336
## [9,] 0.10194613 4.777040 -9.447546 12.483608 0.334
## [10,] -1.25182172 8.250094 -17.901721 11.479718 0.376
## [11,] -1.82782653 6.595916 -18.275559 8.724371 0.376
## [12,] -1.36762029 6.085761 -14.170951 5.396575 0.348
## [13,] -2.13267396 6.748211 -20.167041 5.214743 0.344
## [14,] -0.30514401 4.956926 -11.058168 11.052763 0.290
## [15,] -1.30796494 5.087459 -14.437606 7.237096 0.344
## [16,] -0.89661097 5.145199 -13.904670 9.377070 0.328
## [17,] -5.04483807 13.520294 -53.648764 3.448858 0.398
## [18,] -0.85045895 5.610258 -12.243419 9.569949 0.360
## [19,] -0.98827795 5.354069 -15.747970 10.067388 0.324
## [20,] -0.76106064 5.467010 -12.798167 8.479743 0.322plot(fit.npb.14$beta[,1], type = "l")
plot(fit.npb.14$beta[,2], type = "l")
plot(fit.npb.14$beta[,13], type = "l")
4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1
Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1
4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1
priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 1)
fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.1069866 6.030672 -10.554858 13.131595 0.238
## [2,] -3.5388600 11.344879 -45.538900 4.235505 0.322
## [3,] -0.4768194 4.979254 -12.315786 9.407688 0.228
## [4,] -1.0777163 6.297829 -15.527336 7.048780 0.254
## [5,] 0.3079882 4.895994 -9.898415 16.016525 0.232
## [6,] -0.1230844 3.855826 -9.979027 8.495729 0.230
## [7,] 0.3294762 4.952409 -9.520599 12.258212 0.276
## [8,] 2.5225039 9.778397 -7.572233 32.624945 0.288
## [9,] 0.6895912 5.797225 -8.017044 18.542429 0.228
## [10,] -1.6739128 14.608443 -31.912931 10.597203 0.256
## [11,] -1.7041623 8.389439 -30.507136 7.118220 0.292
## [12,] -1.0759523 5.811060 -14.993317 7.160186 0.258
## [13,] -0.9631344 5.189698 -14.977589 7.118220 0.230
## [14,] 0.0395097 5.946596 -11.826354 16.200728 0.248
## [15,] -1.1190244 5.436167 -19.009897 4.634652 0.260
## [16,] -0.4465094 5.720176 -15.167128 10.170565 0.232
## [17,] -8.0200614 17.258083 -60.986895 2.233433 0.396
## [18,] -0.7233699 5.161727 -12.113457 6.502124 0.228
## [19,] -0.4769079 4.910888 -12.700919 5.732387 0.220
## [20,] 0.3297563 5.004282 -8.627797 15.102298 0.218plot(fit.npb.23$beta[,1], type = "l")
plot(fit.npb.23$beta[,2], type = "l")
plot(fit.npb.23$beta[,13], type = "l")
4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.20117972 6.920473 -13.792067 16.532333 0.286
## [2,] -3.98882121 13.190570 -43.891631 9.065042 0.348
## [3,] 0.17442788 5.128045 -9.260313 10.267010 0.282
## [4,] -1.13850944 4.585463 -13.045164 4.488906 0.276
## [5,] -0.15484197 4.533380 -8.180444 10.249189 0.256
## [6,] -0.03074158 6.282936 -14.832899 15.504284 0.308
## [7,] 0.55075729 5.977633 -9.412162 16.585197 0.282
## [8,] 4.22828783 13.293880 -8.027037 45.654245 0.356
## [9,] 0.48536245 6.617803 -9.142538 16.297567 0.298
## [10,] -0.54331277 16.949724 -21.248630 9.829122 0.334
## [11,] -2.01883982 8.870233 -27.357571 8.607479 0.312
## [12,] -1.41256936 6.005920 -19.418836 6.594701 0.320
## [13,] -1.54081159 5.745344 -16.976281 6.777589 0.306
## [14,] -0.27200502 4.375811 -10.028084 10.075541 0.290
## [15,] -0.87900623 5.050577 -12.279666 5.793930 0.276
## [16,] -0.74731445 5.077872 -12.407591 9.017995 0.288
## [17,] -6.89760808 14.776273 -54.172143 2.518153 0.422
## [18,] -0.72376261 5.343980 -12.102634 9.470188 0.320
## [19,] -0.71784886 4.489023 -11.583507 5.675548 0.250
## [20,] -0.25308924 6.661631 -11.952993 13.177638 0.306plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
4.2 Fit the NPB model
Below I’ve used the 24th set of priors and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "pct_tree_cover"
## [4] "pct_impervious" "mean_aadt_intensity" "dist_m_tri"
## [7] "dist_m_npl" "dist_m_waste_site" "dist_m_major_emit"
## [10] "dist_m_cafo" "dist_m_mine_well" "cvd_rate_adj"
## [13] "res_rate_adj" "violent_crime_rate" "property_crime_rate"
## [16] "pct_less_hs" "pct_unemp" "pct_limited_eng"
## [19] "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v3.1.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v3.1.rdata"))
npb.sum <- summary(fit.npb)4.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum$main.effects) <- colnames(X.scaled)
npb.sum$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -0.39837259 5.706922 -14.272077 13.023276 0.2316
## mean_o3 -71.80706190 93.884623 -264.254977 12.372492 0.6048
## pct_tree_cover 0.03367814 6.086329 -13.793967 15.494484 0.2356
## pct_impervious -1.34207610 5.910994 -18.462241 6.529494 0.2460
## mean_aadt_intensity 0.25489116 5.171531 -9.959488 13.922798 0.2220
## dist_m_tri -0.31617476 5.423478 -13.572703 12.023496 0.2232
## dist_m_npl 0.34482520 5.632786 -10.088418 13.552340 0.2052
## dist_m_waste_site 3.61995576 11.756139 -6.346655 44.627720 0.2732
## dist_m_major_emit 0.70834014 5.967465 -8.596854 17.429979 0.2236
## dist_m_cafo -2.19539809 16.092387 -32.777890 17.414786 0.2812
## dist_m_mine_well -2.25982667 7.981283 -26.647074 6.947264 0.2840
## cvd_rate_adj -1.65938278 7.117165 -21.911126 5.916137 0.2540
## res_rate_adj -2.14263404 7.216720 -24.799903 5.059980 0.2716
## violent_crime_rate -0.11310820 5.863106 -12.216716 13.045736 0.2180
## property_crime_rate -1.05580099 5.655726 -15.784983 8.005556 0.2448
## pct_less_hs -1.05396646 6.050934 -16.755494 6.638840 0.2364
## pct_unemp -6.75999096 15.664698 -56.910641 2.691673 0.3736
## pct_limited_eng -0.88182672 5.539078 -15.381236 8.522579 0.2276
## pct_hh_pov -1.10915865 6.305950 -17.842206 7.134635 0.2376
## pct_poc -0.20029315 6.599061 -14.007899 13.146894 0.2336npb.sum$main.effects$exp <- rownames(npb.sum$main.effects)## Warning in npb.sum$main.effects$exp <- rownames(npb.sum$main.effects): Coercing
## LHS to a listwrite_csv(as.data.frame(npb.sum$main.effects), here::here("Results", "NPB_Main_Effects_Birth_Weight.csv"))
#' Which one's have PIPs > 0.5
# selected_exp <- which(npb.sum$main.effects[,"PIP"] >= 0.5)
# selected_exp4.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum$covariates)[2:nrow(npb.sum$covariates)] <- colnames(W.scaled2)
npb.sum$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3146.452343 225.97454 2709.652796 3579.548597
## lat 5.645610 317.28054 -604.080587 660.851465
## lon 12.489767 150.05028 -295.553464 309.569537
## lat_lon_int 17.252076 382.70962 -720.755345 814.698126
## latina_re -101.467339 48.72339 -193.198203 -1.975895
## black_re -285.841086 52.21589 -387.269403 -184.829173
## other_re -90.002029 69.66488 -230.539406 43.853024
## ed_no_hs 169.252583 78.65201 16.687355 329.982048
## ed_hs 134.418719 68.50548 -2.999718 265.891887
## ed_aa 73.915584 61.60229 -47.235816 191.496946
## ed_4yr 75.069952 51.68029 -29.555363 176.534513
## low_bmi -77.911064 93.05576 -257.442297 107.150476
## ovwt_bmi 41.907731 40.70922 -35.540621 122.145262
## obese_bmi 110.723328 47.14220 18.981498 202.992159
## concep_spring -45.166244 103.33537 -225.606325 136.822189
## concep_summer -34.419393 132.11114 -330.589296 134.365050
## concep_fall 13.030813 82.64904 -173.724167 147.899669
## concep_2010 36.749405 220.88156 -397.977090 474.971289
## concep_2011 25.258876 219.99347 -401.048061 459.141467
## concep_2012 18.384622 222.77447 -409.841086 454.625550
## concep_2013 96.290053 220.01632 -339.191933 526.230486
## maternal_age 63.723277 22.96201 17.811356 108.867189
## any_smoker -123.796366 64.58023 -242.560577 9.817701
## smokeSH -108.197820 44.76502 -195.945720 -21.621077
## mean_cpss 9.403762 19.68199 -29.800179 47.611745
## mean_epsd -51.310438 20.12298 -89.962305 -10.274397
## male 166.080054 33.49731 99.536081 229.837815npb.sum$covariates$covar <- rownames(npb.sum$covariates)## Warning in npb.sum$covariates$covar <- rownames(npb.sum$covariates): Coercing
## LHS to a listwrite_csv(as.data.frame(npb.sum$covariates), here::here("Results", "NPB_Covariate_Effects_Birth_Weight.csv"))4.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.00852215445 0.37326203 0.0000 0.0000 0.0020
## [2,] 0.01246066779 0.52231082 0.0000 0.0000 0.0036
## [3,] -0.00857544475 0.43086228 0.0000 0.0000 0.0024
## [4,] 0.01200773299 0.43735746 0.0000 0.0000 0.0028
## [5,] 0.02133322904 0.52229780 0.0000 0.0000 0.0024
## [6,] -0.00159817433 0.30823571 0.0000 0.0000 0.0024
## [7,] -0.00358887092 0.44827747 0.0000 0.0000 0.0036
## [8,] -0.01524024738 0.81409452 0.0000 0.0000 0.0016
## [9,] -0.02273428101 0.87219171 0.0000 0.0000 0.0012
## [10,] -0.01680612251 0.56706332 0.0000 0.0000 0.0012
## [11,] 0.00069135071 0.03456754 0.0000 0.0000 0.0004
## [12,] -0.02026199314 0.59508189 0.0000 0.0000 0.0024
## [13,] -0.00390810510 0.22788632 0.0000 0.0000 0.0028
## [14,] -0.02534220377 0.54603620 0.0000 0.0000 0.0028
## [15,] -0.00226728366 0.31987735 0.0000 0.0000 0.0020
## [16,] -0.00370424994 0.30022571 0.0000 0.0000 0.0020
## [17,] -0.01013069933 0.50653497 0.0000 0.0000 0.0004
## [18,] -0.00732528715 0.48172079 0.0000 0.0000 0.0036
## [19,] 0.00548247397 0.30748879 0.0000 0.0000 0.0012
## [20,] -0.00008835512 0.18914950 0.0000 0.0000 0.0020
## [21,] 0.00422595015 0.21503826 0.0000 0.0000 0.0016
## [22,] 0.00000000000 0.00000000 0.0000 0.0000 0.0000
## [23,] -0.04815352484 1.21713332 0.0000 0.0000 0.0032
## [24,] -0.00494479757 0.51132961 0.0000 0.0000 0.0008
## [25,] -0.07745324239 1.59860588 0.0000 0.0000 0.0040
## [26,] 0.00366372004 0.18318600 0.0000 0.0000 0.0004
## [27,] -0.09553872222 1.83606876 0.0000 0.0000 0.0048
## [28,] -0.04064048904 0.81042860 0.0000 0.0000 0.0036
## [29,] 0.01122095306 0.54117256 0.0000 0.0000 0.0016
## [30,] -0.00832011097 0.33120848 0.0000 0.0000 0.0012
## [31,] 0.00606721021 0.42728042 0.0000 0.0000 0.0016
## [32,] -0.01062203310 0.28249997 0.0000 0.0000 0.0020
## [33,] 0.01577733949 0.77172169 0.0000 0.0000 0.0024
## [34,] 0.00799471556 0.32842418 0.0000 0.0000 0.0016
## [35,] 0.00515382669 0.42805758 0.0000 0.0000 0.0016
## [36,] 0.02864710521 0.66767430 0.0000 0.0000 0.0024
## [37,] 0.01731419885 0.61579742 0.0000 0.0000 0.0016
## [38,] -0.00173809030 0.41739057 0.0000 0.0000 0.0024
## [39,] -0.00167930673 0.06972500 0.0000 0.0000 0.0008
## [40,] -0.00492535313 0.57678176 0.0000 0.0000 0.0020
## [41,] 0.00154606481 0.27353512 0.0000 0.0000 0.0016
## [42,] -0.00549857939 0.24670602 0.0000 0.0000 0.0012
## [43,] -0.00284522459 0.22688334 0.0000 0.0000 0.0016
## [44,] -0.00018029778 0.08981227 0.0000 0.0000 0.0008
## [45,] -0.04519288653 1.16306458 0.0000 0.0000 0.0036
## [46,] 0.00251325603 0.33176290 0.0000 0.0000 0.0020
## [47,] 0.01042665769 0.97184859 0.0000 0.0000 0.0016
## [48,] -0.00454133566 0.43281952 0.0000 0.0000 0.0012
## [49,] -0.00136538119 0.23713005 0.0000 0.0000 0.0020
## [50,] 0.02845914613 0.99514444 0.0000 0.0000 0.0032
## [51,] 0.00377009273 0.58557318 0.0000 0.0000 0.0028
## [52,] -0.00117229336 0.15087522 0.0000 0.0000 0.0020
## [53,] 0.02745358268 1.55278260 0.0000 0.0000 0.0012
## [54,] 0.00018292834 0.51781716 0.0000 0.0000 0.0016
## [55,] 0.02683886892 0.75962445 0.0000 0.0000 0.0028
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## [622,] -0.19286966594 3.76289013 0.0000 0.0000 0.0064
## [623,] -0.05443974094 2.06035293 0.0000 0.0000 0.0020
## [624,] -0.04038764877 0.99933868 0.0000 0.0000 0.0032
## [625,] 0.00411212282 0.33655114 0.0000 0.0000 0.0032
## [626,] 0.00262265315 0.13113266 0.0000 0.0000 0.0004
## [627,] -0.01693170606 0.45041393 0.0000 0.0000 0.0036
## [628,] -0.00809910132 0.42957659 0.0000 0.0000 0.0016
## [629,] -0.04589090208 0.98951040 0.0000 0.0000 0.0036
## [630,] -0.00121992104 0.25501943 0.0000 0.0000 0.0016
## [631,] 0.00036591234 0.01829562 0.0000 0.0000 0.0004
## [632,] -0.17257243953 3.08728681 0.0000 0.0000 0.0080
## [633,] -0.01107524767 0.46911352 0.0000 0.0000 0.0020
## [634,] -0.02017955861 1.02304984 0.0000 0.0000 0.0012
## [635,] -0.01295070475 0.57375942 0.0000 0.0000 0.0020
## [636,] -0.00713746392 0.56751840 0.0000 0.0000 0.0024
## [637,] -0.03376105122 1.17020773 0.0000 0.0000 0.0024
## [638,] -0.00989327328 0.33591242 0.0000 0.0000 0.0020
## [639,] -0.00256533956 0.36739966 0.0000 0.0000 0.0016
## [640,] -0.00269028292 0.37933905 0.0000 0.0000 0.0012
## [641,] -0.00963783906 1.03972071 0.0000 0.0000 0.0024
## [642,] -0.02124043579 1.04050109 0.0000 0.0000 0.0016
## [643,] -0.00013314138 0.33137009 0.0000 0.0000 0.0020
## [644,] 0.00115447198 0.52930014 0.0000 0.0000 0.0016
## [645,] 0.01349330416 0.79277828 0.0000 0.0000 0.0028
## [646,] -0.13146962722 2.90184766 0.0000 0.0000 0.0040
## [647,] -0.00844679896 0.69038141 0.0000 0.0000 0.0020
## [648,] 0.00148019569 0.33650714 0.0000 0.0000 0.0024
## [649,] 0.00107936657 0.49317648 0.0000 0.0000 0.0028
## [650,] -0.04838680123 1.09978452 0.0000 0.0000 0.0028
## [651,] 0.00002731102 0.34128801 0.0000 0.0000 0.0016
## [652,] -0.00983561295 0.33562587 0.0000 0.0000 0.0012
## [653,] 0.01361635077 0.40605488 0.0000 0.0000 0.0012
## [654,] -0.00192308137 0.16579172 0.0000 0.0000 0.0008
## [655,] -0.02944831288 1.41661508 0.0000 0.0000 0.0008
## [656,] -0.01037220382 0.31893413 0.0000 0.0000 0.0024
## [657,] -0.00925471576 0.60974452 0.0000 0.0000 0.0036
## [658,] 0.00527591694 0.26379585 0.0000 0.0000 0.0004
## [659,] -0.00335552470 0.52713649 0.0000 0.0000 0.0024
## [660,] -0.01209702695 0.59328194 0.0000 0.0000 0.0020
## [661,] -0.01733385276 0.84580107 0.0000 0.0000 0.0036
## [662,] -0.00896371809 0.55639967 0.0000 0.0000 0.0024
## [663,] 0.00924620893 0.34937777 0.0000 0.0000 0.0024
## [664,] -0.00087552466 0.36674731 0.0000 0.0000 0.0012
## [665,] -0.01040482765 0.99927262 0.0000 0.0000 0.0024
## [666,] 0.00480427342 0.21088040 0.0000 0.0000 0.0008
## [667,] 0.00298379021 0.13215909 0.0000 0.0000 0.0008
## [668,] 0.00354924993 0.19650710 0.0000 0.0000 0.0020
## [669,] -0.10424088377 3.77536817 0.0000 0.0000 0.0032
## [670,] -0.00727880764 0.80374376 0.0000 0.0000 0.0028
## [671,] 0.00621117048 0.31055852 0.0000 0.0000 0.0004
## [672,] 0.00842008502 0.35715397 0.0000 0.0000 0.0016
## [673,] -0.00265938357 0.20680760 0.0000 0.0000 0.0008
## [674,] -0.00501152234 0.69124209 0.0000 0.0000 0.0036
## [675,] -0.00355356612 0.37285235 0.0000 0.0000 0.0016
## [676,] -0.00513795454 0.45422770 0.0000 0.0000 0.0028
## [677,] 0.38405494940 5.57276673 0.0000 0.0000 0.0072
## [678,] -0.01395056082 0.67612886 0.0000 0.0000 0.0020
## [679,] -0.00669660542 0.49493155 0.0000 0.0000 0.0016
## [680,] -0.01556330413 0.47298986 0.0000 0.0000 0.0016
## [681,] 0.00629475283 0.29087253 0.0000 0.0000 0.0008
## [682,] -0.00088703025 0.04435151 0.0000 0.0000 0.0004
## [683,] -0.01796041531 0.89802077 0.0000 0.0000 0.0004
## [684,] -0.04612964407 0.90773034 0.0000 0.0000 0.0040
## [685,] -0.01850991613 0.47486439 0.0000 0.0000 0.0032
## [686,] -0.03578881374 1.03637612 0.0000 0.0000 0.0024
## [687,] -0.00102821255 0.17560270 0.0000 0.0000 0.0016
## [688,] -0.03315282258 0.81850228 0.0000 0.0000 0.0020
## [689,] 0.00363826223 0.18625282 0.0000 0.0000 0.0016
## [690,] -0.01099718786 1.51015482 0.0000 0.0000 0.0024
## [691,] -0.01716996373 0.82623306 0.0000 0.0000 0.0032
## [692,] 0.03075069310 1.98626552 0.0000 0.0000 0.0016
## [693,] -0.00786662130 0.28496282 0.0000 0.0000 0.0008
## [694,] -0.01686672059 0.75953854 0.0000 0.0000 0.0028
## [695,] 0.02823695619 2.08139949 0.0000 0.0000 0.0032
## [696,] 0.03124882673 1.93904513 0.0000 0.0000 0.0024
## [697,] -0.00846355312 0.60931349 0.0000 0.0000 0.0024
## [698,] -0.04285784756 1.60880208 0.0000 0.0000 0.0016
## [699,] 0.01736235986 0.62512042 0.0000 0.0000 0.0016
## [700,] -0.09184617746 2.30101104 0.0000 0.0000 0.0044
## [701,] -0.01214252302 0.73769567 0.0000 0.0000 0.0020
## [702,] -0.37227601981 5.56141530 0.0000 0.0000 0.0080
## [703,] 1.05503591250 11.61964145 0.0000 0.0000 0.0112
## [704,] -0.00355271823 0.26910166 0.0000 0.0000 0.0012
## [705,] -0.00537482556 0.33114357 0.0000 0.0000 0.0016
## [706,] -0.05631042818 2.46432860 0.0000 0.0000 0.0012
## [707,] -0.00188057696 0.51914149 0.0000 0.0000 0.0020
## [708,] -0.01662849038 0.51727536 0.0000 0.0000 0.0028
## [709,] -0.00337402209 0.23792173 0.0000 0.0000 0.0012
## [710,] -0.01444002128 0.35382363 0.0000 0.0000 0.00204.2.4 Predict fitted values for each individual
pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals4.2.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")
4.3 Fit the NPB model without ozone
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "pct_tree_cover"
## [4] "pct_impervious" "mean_aadt_intensity" "dist_m_tri"
## [7] "dist_m_npl" "dist_m_waste_site" "dist_m_major_emit"
## [10] "dist_m_cafo" "dist_m_mine_well" "cvd_rate_adj"
## [13] "res_rate_adj" "violent_crime_rate" "property_crime_rate"
## [16] "pct_less_hs" "pct_unemp" "pct_limited_eng"
## [19] "pct_hh_pov" "pct_poc"X.scaled2 <- X.scaled[,-c(2)]
colnames(X.scaled2)## [1] "mean_pm" "pct_tree_cover" "pct_impervious"
## [4] "mean_aadt_intensity" "dist_m_tri" "dist_m_npl"
## [7] "dist_m_waste_site" "dist_m_major_emit" "dist_m_cafo"
## [10] "dist_m_mine_well" "cvd_rate_adj" "res_rate_adj"
## [13] "violent_crime_rate" "property_crime_rate" "pct_less_hs"
## [16] "pct_unemp" "pct_limited_eng" "pct_hh_pov"
## [19] "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled2, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v3.2.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v3.2.rdata"))
npb.sum2 <- summary(fit.npb2)4.3.1 First, main effect regression coefficients with PIPs
rownames(npb.sum2$main.effects) <- colnames(X.scaled2)
npb.sum2$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm 0.4407640 6.481440 -12.161629 18.073865 0.2564
## pct_tree_cover 0.2642844 5.907754 -12.367591 15.955959 0.2508
## pct_impervious -0.9324881 6.452437 -17.545274 9.331679 0.2380
## mean_aadt_intensity 0.4357418 5.601033 -10.521010 15.787301 0.2464
## dist_m_tri 0.1581616 6.262555 -13.957391 16.556472 0.2772
## dist_m_npl 1.1673370 6.973845 -9.358043 22.024409 0.2660
## dist_m_waste_site 4.8288396 12.792222 -6.853881 45.524547 0.3356
## dist_m_major_emit 1.3269033 7.462049 -9.148800 25.099342 0.2588
## dist_m_cafo -1.9694753 18.626634 -42.182813 24.084298 0.3276
## dist_m_mine_well -2.0373787 9.241124 -29.332014 10.564666 0.2944
## cvd_rate_adj -1.1051803 6.716039 -19.079850 9.810397 0.2676
## res_rate_adj -1.6056014 7.214406 -23.176058 8.434401 0.2684
## violent_crime_rate 0.2620968 5.943370 -10.631896 15.787301 0.2528
## property_crime_rate -1.0638364 5.922815 -18.092789 8.630678 0.2536
## pct_less_hs -0.5034778 7.128440 -16.487666 14.445030 0.2748
## pct_unemp -9.3706142 19.159359 -67.673376 3.109754 0.4120
## pct_limited_eng -0.6049911 6.549114 -15.795377 11.534563 0.2500
## pct_hh_pov -0.3708097 6.801363 -15.364005 12.755524 0.2524
## pct_poc 0.3869594 7.286020 -13.829870 19.624174 0.2720#' Which one's have PIPs > 0.5
# selected_exp2 <- which(npb.sum2$main.effects[,"PIP"] >= 0.5)
# selected_exp24.3.2 Next, posterior means and CIs for covariates
rownames(npb.sum2$covariates)[2:nrow(npb.sum2$covariates)] <- colnames(W.scaled2)
npb.sum2$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3125.11023270 214.75115 2719.334345 3552.668568
## lat -0.08939079 320.45931 -616.952777 636.223438
## lon 15.82732882 153.33967 -286.295896 309.641467
## lat_lon_int 9.24042756 387.83722 -739.040154 765.768868
## latina_re -97.11919556 48.61350 -194.288010 -4.274013
## black_re -290.74018844 53.91405 -392.202850 -183.854057
## other_re -99.50320177 69.67897 -233.173455 30.817102
## ed_no_hs 159.55463623 78.96724 8.513339 313.605512
## ed_hs 120.92695635 70.64099 -15.857060 264.855468
## ed_aa 65.53253757 61.57438 -54.153453 192.640553
## ed_4yr 69.34846410 52.63995 -38.225123 173.909992
## low_bmi -104.76200883 90.82364 -284.118593 74.825986
## ovwt_bmi 37.35735397 41.55616 -42.825391 117.552674
## obese_bmi 105.82183976 46.65106 14.868244 197.989197
## concep_spring -47.50513601 48.23797 -143.934262 46.020343
## concep_summer 51.01158169 48.25005 -44.543078 142.596506
## concep_fall 52.78650721 47.71546 -43.629803 144.301487
## concep_2010 16.18383028 214.32551 -397.478318 425.733197
## concep_2011 -7.90111335 210.94006 -417.994295 397.505258
## concep_2012 -51.38294168 212.32483 -469.020930 362.601018
## concep_2013 71.48878418 213.55200 -352.383385 478.747023
## maternal_age 67.92832298 22.79868 23.543573 113.200444
## any_smoker -131.11644390 65.32648 -260.990044 -1.186657
## smokeSH -104.19291072 44.69544 -190.866866 -17.735269
## mean_cpss 8.98637765 20.19692 -30.186639 47.608133
## mean_epsd -51.28094081 20.31286 -89.775993 -10.622189
## male 160.46939156 33.12251 92.736843 224.5367824.3.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum2$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.00070489986 0.2615722 0 0 0.0040
## [2,] -0.00228693613 0.3715087 0 0 0.0072
## [3,] 0.00647121899 0.5343933 0 0 0.0060
## [4,] 0.00044081434 0.3101090 0 0 0.0060
## [5,] -0.00745209726 0.4937818 0 0 0.0064
## [6,] -0.01560976678 0.4720498 0 0 0.0052
## [7,] -0.01722247659 0.5852312 0 0 0.0068
## [8,] -0.04930647285 1.1052879 0 0 0.0084
## [9,] -0.02526369977 0.8438638 0 0 0.0068
## [10,] -0.01003786971 0.3301583 0 0 0.0052
## [11,] 0.00095854730 0.9508631 0 0 0.0076
## [12,] -0.03813887461 0.9465690 0 0 0.0068
## [13,] -0.03244939866 0.7384257 0 0 0.0056
## [14,] -0.02060545794 0.5279291 0 0 0.0052
## [15,] -0.00884382385 0.3674973 0 0 0.0036
## [16,] -0.04760286638 1.0706389 0 0 0.0076
## [17,] 0.00390734679 0.3389511 0 0 0.0040
## [18,] 0.00283095104 0.5579978 0 0 0.0068
## [19,] 0.00036777783 0.6876817 0 0 0.0060
## [20,] 0.00534721851 0.4136275 0 0 0.0060
## [21,] 0.01819477404 0.5408361 0 0 0.0056
## [22,] 0.00153988848 0.4458849 0 0 0.0048
## [23,] 0.00983877229 0.7662673 0 0 0.0056
## [24,] 0.01327967636 0.5057805 0 0 0.0072
## [25,] -0.01184554525 0.4089115 0 0 0.0064
## [26,] -0.03954456420 0.8499696 0 0 0.0060
## [27,] -0.03552106601 1.0235001 0 0 0.0060
## [28,] -0.00306169494 0.7856794 0 0 0.0052
## [29,] -0.02848579398 0.6073078 0 0 0.0056
## [30,] 0.00553802648 0.3980201 0 0 0.0060
## [31,] -0.05544807950 1.2544435 0 0 0.0052
## [32,] 0.00289600399 0.2860713 0 0 0.0052
## [33,] 0.00096869062 0.5623342 0 0 0.0068
## [34,] -0.00627907970 0.2522949 0 0 0.0040
## [35,] -0.00857757876 0.2359099 0 0 0.0044
## [36,] 0.02350558424 1.1531182 0 0 0.0060
## [37,] 0.03492129619 0.8794809 0 0 0.0080
## [38,] 0.00084278122 0.3552540 0 0 0.0044
## [39,] 0.00765313480 0.4884620 0 0 0.0048
## [40,] 0.01626896815 0.4310151 0 0 0.0056
## [41,] 0.00795417135 0.3789797 0 0 0.0036
## [42,] -0.00999666034 0.5214566 0 0 0.0048
## [43,] -0.01850419331 0.6488152 0 0 0.0040
## [44,] -0.01442520183 0.4369560 0 0 0.0052
## [45,] -0.02109882891 0.5472945 0 0 0.0052
## [46,] -0.00601939666 0.5804819 0 0 0.0056
## [47,] -0.00395211894 0.4725794 0 0 0.0036
## [48,] -0.03881909268 0.8444165 0 0 0.0048
## [49,] 0.01195977696 0.5582980 0 0 0.0076
## [50,] -0.01182785804 0.4862868 0 0 0.0068
## [51,] -0.00873685811 0.2045007 0 0 0.0024
## [52,] -0.00371656961 0.5593697 0 0 0.0064
## [53,] 0.01236884699 0.3599505 0 0 0.0032
## [54,] -0.00309728546 0.2999571 0 0 0.0032
## [55,] 0.04599311665 1.2600665 0 0 0.0052
## [56,] -0.02954062525 0.6218568 0 0 0.0060
## [57,] -0.04559485714 1.0986161 0 0 0.0080
## [58,] -0.06723551558 1.0571497 0 0 0.0092
## [59,] -0.03619309295 0.8931806 0 0 0.0052
## [60,] -0.05971955536 1.0841527 0 0 0.0096
## [61,] -0.03960603157 0.6793694 0 0 0.0064
## [62,] 0.02075926153 0.8585117 0 0 0.0048
## [63,] -0.00557993815 0.5279123 0 0 0.0056
## [64,] 0.01707334964 0.6388643 0 0 0.0092
## [65,] 0.01293984973 0.5391502 0 0 0.0060
## [66,] 0.04169749849 1.1045298 0 0 0.0080
## [67,] -0.00752068963 0.3619287 0 0 0.0060
## [68,] -0.01481281705 0.3604213 0 0 0.0064
## [69,] 0.01830690909 0.3966702 0 0 0.0052
## [70,] -0.00752346119 0.3411635 0 0 0.0068
## [71,] -0.02449631332 0.8634536 0 0 0.0080
## [72,] 0.02037321089 0.5818778 0 0 0.0048
## [73,] 0.00502085279 0.3602976 0 0 0.0044
## [74,] -0.00249885312 0.5100230 0 0 0.0076
## [75,] 0.01009107123 0.5002083 0 0 0.0036
## [76,] -0.00422637989 0.5636386 0 0 0.0076
## [77,] 0.01431627035 0.6027884 0 0 0.0072
## [78,] 0.04900323863 1.7263292 0 0 0.0068
## [79,] -0.00926932812 0.7337227 0 0 0.0052
## [80,] 0.00037742863 0.2155910 0 0 0.0036
## [81,] -0.00261599525 0.3441624 0 0 0.0036
## [82,] -0.00459069147 0.4074966 0 0 0.0052
## [83,] -0.00312319212 0.3472492 0 0 0.0064
## [84,] -0.00502038697 0.5803227 0 0 0.0072
## [85,] -0.00092574006 0.4456749 0 0 0.0048
## [86,] 0.00071849739 0.7735737 0 0 0.0056
## [87,] -0.00564820929 0.3948624 0 0 0.0056
## [88,] -0.01186822075 0.3374591 0 0 0.0076
## [89,] -0.01747643069 0.8364548 0 0 0.0080
## [90,] -0.00031630302 0.2228517 0 0 0.0032
## [91,] -0.00513956643 0.5465570 0 0 0.0044
## [92,] -0.02032438390 0.5379958 0 0 0.0060
## [93,] -0.01771887427 0.4873413 0 0 0.0072
## [94,] 0.04650096556 1.3776472 0 0 0.0064
## [95,] 0.01236704805 0.4577457 0 0 0.0060
## [96,] -0.00331224680 0.5194041 0 0 0.0088
## [97,] -0.01499898251 0.6970688 0 0 0.0044
## [98,] 0.00281379055 0.5895343 0 0 0.0064
## [99,] 0.00139653498 0.5079189 0 0 0.0052
## [100,] 0.00120670233 0.9336013 0 0 0.0084
## [101,] -0.02641595216 0.5640905 0 0 0.0072
## [102,] 0.00398614422 0.7135476 0 0 0.0084
## [103,] 0.01793837783 0.7336196 0 0 0.0056
## [104,] 0.01650775948 0.9337035 0 0 0.0060
## [105,] -0.00655069219 0.4279052 0 0 0.0036
## [106,] 0.06058987851 1.1328023 0 0 0.0068
## [107,] 0.09911197562 2.0512419 0 0 0.0096
## [108,] -0.02891819707 0.8225235 0 0 0.0068
## [109,] -0.00231398495 0.4151320 0 0 0.0052
## [110,] 0.00154357333 0.7002825 0 0 0.0056
## [111,] -0.02620142600 0.8172581 0 0 0.0068
## [112,] -0.05705722631 1.1805650 0 0 0.0080
## [113,] -0.06392313596 1.0213473 0 0 0.0076
## [114,] -0.03846456579 0.7170430 0 0 0.0060
## [115,] -0.02171772408 0.6109252 0 0 0.0048
## [116,] -0.03653445798 0.8464495 0 0 0.0084
## [117,] -0.13397927382 1.7740826 0 0 0.0108
## [118,] -0.01138691331 0.4832909 0 0 0.0056
## [119,] -0.00884811397 0.4199687 0 0 0.0048
## [120,] 0.00632859515 0.9014699 0 0 0.0068
## [121,] -0.05077466301 1.0327486 0 0 0.0080
## [122,] 0.00765786788 0.6810144 0 0 0.0064
## [123,] -0.00196373832 0.2702260 0 0 0.0036
## [124,] -0.00125093108 0.1620005 0 0 0.0024
## [125,] -0.02800549721 0.8822045 0 0 0.0076
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## [449,] -0.04449943103 1.4642250 0 0 0.0080
## [450,] 0.16188414135 3.8197252 0 0 0.0064
## [451,] -0.03524443625 1.1359170 0 0 0.0116
## [452,] -0.01990260308 0.7470221 0 0 0.0064
## [453,] -0.03563036555 1.3974746 0 0 0.0068
## [454,] -0.01334478992 0.6322938 0 0 0.0076
## [455,] -0.00367619342 0.5538738 0 0 0.0068
## [456,] -0.00006125757 0.2967185 0 0 0.0032
## [457,] -0.01209037474 0.3712565 0 0 0.0068
## [458,] -0.01582636745 0.8284683 0 0 0.0028
## [459,] -0.01293041925 0.6712189 0 0 0.0072
## [460,] -0.00518261084 0.8897577 0 0 0.0084
## [461,] -0.00508757319 0.5167030 0 0 0.0068
## [462,] -0.03484757347 1.1241169 0 0 0.0092
## [463,] -0.00712172466 0.9957859 0 0 0.0064
## [464,] -0.01667477189 1.0489156 0 0 0.0084
## [465,] -0.03109496372 0.7651378 0 0 0.0068
## [466,] 0.01326239709 1.8389412 0 0 0.0088
## [467,] -0.09229224475 2.1979405 0 0 0.0064
## [468,] -0.13297873048 2.8302727 0 0 0.0076
## [469,] -0.01103157437 0.7752234 0 0 0.0072
## [470,] -0.04547131929 1.2587517 0 0 0.0060
## [471,] -0.02307593859 0.9544587 0 0 0.0068
## [472,] 0.00072421055 0.7609569 0 0 0.0052
## [473,] -0.05656765068 1.2484350 0 0 0.0080
## [474,] -0.16233579405 2.6856251 0 0 0.0128
## [475,] -0.05389028191 1.8045395 0 0 0.0076
## [476,] 0.15019211600 3.6620655 0 0 0.0080
## [477,] -0.01027060226 0.7427028 0 0 0.0076
## [478,] -0.02195210358 0.8420569 0 0 0.0044
## [479,] -0.12740440841 5.1090053 0 0 0.0076
## [480,] -0.00315784356 1.1006213 0 0 0.0068
## [481,] -0.00304373186 0.4930666 0 0 0.0036
## [482,] 0.01309693031 0.4072924 0 0 0.0040
## [483,] -0.01077890501 0.7246331 0 0 0.0064
## [484,] -0.00661770813 0.8091020 0 0 0.0084
## [485,] -0.01086101909 0.5181647 0 0 0.0048
## [486,] -0.04161252142 1.0410161 0 0 0.0060
## [487,] -0.01826561656 0.7494178 0 0 0.0040
## [488,] -0.01886838556 0.9513777 0 0 0.0072
## [489,] 0.14165423128 6.0433113 0 0 0.0100
## [490,] 0.00234704590 0.3789781 0 0 0.0052
## [491,] 0.01743115056 1.3320420 0 0 0.0048
## [492,] -0.00344186691 0.2189310 0 0 0.0048
## [493,] -0.10935767998 2.1997432 0 0 0.0064
## [494,] -0.59483802723 14.3227313 0 0 0.0084
## [495,] -0.03901635091 0.8489960 0 0 0.0064
## [496,] 0.00837063695 1.2941352 0 0 0.0060
## [497,] 0.05805973173 1.3414036 0 0 0.0068
## [498,] 0.00131566611 0.4723066 0 0 0.0052
## [499,] 0.02033275496 0.8233152 0 0 0.0068
## [500,] 0.00347819425 0.4456547 0 0 0.0044
## [501,] -0.05697984234 1.4784239 0 0 0.0088
## [502,] 0.05768477067 2.1187869 0 0 0.0052
## [503,] 0.00527309451 0.6978629 0 0 0.0060
## [504,] -0.01062213511 0.3668426 0 0 0.0060
## [505,] -0.03498916969 0.9107845 0 0 0.0064
## [506,] -0.00256779852 0.8114997 0 0 0.0056
## [507,] -0.10205217111 1.9428381 0 0 0.0132
## [508,] -0.02611995466 0.5678791 0 0 0.0084
## [509,] -0.04751296707 2.0919006 0 0 0.0088
## [510,] -0.00287951151 0.7745983 0 0 0.0064
## [511,] 0.00113898006 0.2753092 0 0 0.0048
## [512,] -0.02444767007 0.8664069 0 0 0.0072
## [513,] -0.00606287706 1.0794713 0 0 0.0076
## [514,] -0.11029107481 3.5512830 0 0 0.0044
## [515,] 0.28258265146 10.0694140 0 0 0.0072
## [516,] -0.10031007749 4.9097686 0 0 0.0088
## [517,] -0.06244952542 2.0918973 0 0 0.0068
## [518,] 0.02305944125 1.2326754 0 0 0.0056
## [519,] -0.05987911429 1.4553599 0 0 0.0068
## [520,] -0.11906474785 4.2424177 0 0 0.0080
## [521,] -0.14453943388 2.8835544 0 0 0.0108
## [522,] 0.02173356275 0.7212922 0 0 0.0056
## [523,] 0.01129156554 0.5012139 0 0 0.0036
## [524,] -0.01042194281 0.5293519 0 0 0.0084
## [525,] -0.01536968497 0.7271904 0 0 0.0056
## [526,] -0.04404686419 1.9728043 0 0 0.0068
## [527,] -0.00632791765 0.9339384 0 0 0.0092
## [528,] -0.03705217161 0.8099271 0 0 0.0048
## [529,] -0.01348837922 0.6945416 0 0 0.0060
## [530,] 0.03256597547 0.8233571 0 0 0.0060
## [531,] 0.00433042817 0.8778111 0 0 0.0080
## [532,] -0.02684805637 0.9463427 0 0 0.0056
## [533,] -0.08246887237 1.5292165 0 0 0.0088
## [534,] -0.01886106065 0.7569910 0 0 0.0060
## [535,] -0.05144934758 1.2555387 0 0 0.0080
## [536,] -0.00099964129 0.5883518 0 0 0.0052
## [537,] -0.06475441667 1.4126420 0 0 0.0068
## [538,] -0.02251677833 0.8307205 0 0 0.0072
## [539,] -0.01358603036 0.5788411 0 0 0.0060
## [540,] 0.01900190000 1.1585567 0 0 0.0076
## [541,] -0.02279796865 0.7112741 0 0 0.0044
## [542,] -0.02334423527 0.8232008 0 0 0.0068
## [543,] 0.03083240425 0.9701480 0 0 0.0060
## [544,] -0.03739440537 1.3359142 0 0 0.0092
## [545,] -0.06186586131 1.3161702 0 0 0.0080
## [546,] -0.00788504592 1.4848881 0 0 0.0072
## [547,] 0.10037175021 2.6271471 0 0 0.0088
## [548,] 0.01033344274 0.5416129 0 0 0.0048
## [549,] -0.09288551530 2.9735232 0 0 0.0076
## [550,] 0.00072463394 0.6618185 0 0 0.0044
## [551,] -0.10218023774 2.2758304 0 0 0.0072
## [552,] -0.00968645740 0.7425965 0 0 0.0064
## [553,] -0.09180750490 1.9950580 0 0 0.0092
## [554,] 0.14817095904 3.2651406 0 0 0.0072
## [555,] -0.10806249737 2.2329092 0 0 0.0088
## [556,] 0.00392828102 0.5700473 0 0 0.0092
## [557,] -0.01980664286 0.5053938 0 0 0.0060
## [558,] 0.05307375585 1.5622932 0 0 0.0068
## [559,] -0.02246959669 0.7922375 0 0 0.0080
## [560,] 0.00805816887 0.4324853 0 0 0.0064
## [561,] -0.03274436257 0.9539404 0 0 0.0072
## [562,] 0.00393151581 0.7113762 0 0 0.0044
## [563,] -0.03638787429 0.8537371 0 0 0.0084
## [564,] -0.06701297344 1.1124659 0 0 0.0080
## [565,] -0.07725131918 2.2615023 0 0 0.0096
## [566,] -0.00928118976 0.7858176 0 0 0.0060
## [567,] -0.03335090435 0.7809843 0 0 0.0040
## [568,] -0.14840499101 3.9228124 0 0 0.0092
## [569,] -0.01861345176 0.5506965 0 0 0.0088
## [570,] -0.02361738580 0.7139254 0 0 0.0072
## [571,] -0.14502999830 2.9696430 0 0 0.0072
## [572,] -0.03580922781 1.1655563 0 0 0.0060
## [573,] -0.05951573900 1.3704253 0 0 0.0064
## [574,] -0.01424506487 0.8366104 0 0 0.0068
## [575,] -0.04016379260 1.6506645 0 0 0.0072
## [576,] -0.02413716008 0.6051806 0 0 0.0052
## [577,] -0.15027500818 2.8389735 0 0 0.0076
## [578,] -0.05556391348 1.2316867 0 0 0.0080
## [579,] -0.09997429333 1.7019048 0 0 0.0100
## [580,] 0.00360443450 0.9967971 0 0 0.0048
## [581,] -0.02038420876 0.7872548 0 0 0.0044
## [582,] -0.01322948473 0.5084871 0 0 0.0068
## [583,] -0.02400532523 0.7729448 0 0 0.0064
## [584,] -0.09079851712 1.9482808 0 0 0.0076
## [585,] -0.00869038460 0.4732573 0 0 0.0056
## [586,] 0.01287399401 0.4050116 0 0 0.0064
## [587,] -0.28517640587 4.0119864 0 0 0.0128
## [588,] -0.02657993511 1.0656853 0 0 0.0052
## [589,] -0.15732143483 2.5128629 0 0 0.0092
## [590,] -0.02050218167 0.9533988 0 0 0.0064
## [591,] -0.02448282558 0.5783263 0 0 0.0036
## [592,] 0.03067515932 1.2363184 0 0 0.0064
## [593,] 0.01012489384 0.7951166 0 0 0.0068
## [594,] -0.00296578181 0.6174908 0 0 0.0060
## [595,] 0.01958418880 1.4058722 0 0 0.0048
## [596,] -0.02245148855 0.7288340 0 0 0.0060
## [597,] -0.00297965647 0.6886126 0 0 0.0048
## [598,] 0.00826010160 1.5868813 0 0 0.0084
## [599,] -0.00903424632 1.1399129 0 0 0.0072
## [600,] 0.03235800371 1.1119928 0 0 0.0052
## [601,] -0.10242322752 2.2465206 0 0 0.0084
## [602,] -0.02320464626 1.6876933 0 0 0.0076
## [603,] -0.02184780020 0.5963628 0 0 0.0036
## [604,] -0.00151015342 1.5445703 0 0 0.0072
## [605,] -0.13688680542 2.2526437 0 0 0.0120
## [606,] 0.12233961389 3.0290075 0 0 0.0096
## [607,] -0.17022078113 3.2556028 0 0 0.0112
## [608,] -0.01424318968 0.3431607 0 0 0.0048
## [609,] -0.02756855277 1.3592225 0 0 0.0064
## [610,] -0.01835903005 0.8810822 0 0 0.0084
## [611,] -0.02116144171 0.6228565 0 0 0.0052
## [612,] -0.00861212027 0.3816419 0 0 0.0044
## [613,] -0.03644205680 1.2435053 0 0 0.0080
## [614,] -0.00029113491 0.9778448 0 0 0.0072
## [615,] -0.05095436566 1.1801820 0 0 0.0100
## [616,] -0.03644181179 1.0931629 0 0 0.0072
## [617,] 0.01225762336 0.9418062 0 0 0.0080
## [618,] -0.00588046246 0.6369702 0 0 0.0056
## [619,] 0.00732379180 1.6487593 0 0 0.0080
## [620,] -0.01365837600 0.6997623 0 0 0.0068
## [621,] -0.03490604650 1.0929314 0 0 0.0076
## [622,] -0.05382299268 1.3324162 0 0 0.0100
## [623,] -0.02937780475 0.6511281 0 0 0.0056
## [624,] -0.19678922634 5.0153489 0 0 0.0064
## [625,] -0.06102762318 1.4082121 0 0 0.0060
## [626,] -0.01799875044 0.8192186 0 0 0.0092
## [627,] -0.01922824811 0.8426396 0 0 0.0080
## [628,] -0.01942748523 0.4414635 0 0 0.0048
## [629,] -0.10212021527 2.4015833 0 0 0.0076
## [630,] -0.03255109354 1.2734485 0 0 0.0064
## [631,] -0.02162793219 0.6299233 0 0 0.0064
## [632,] 0.38514942054 4.5237266 0 0 0.0152
## [633,] -0.12891188299 2.4083169 0 0 0.0092
## [634,] -0.00553075917 0.6266780 0 0 0.0052
## [635,] -0.05236693722 1.1113923 0 0 0.0056
## [636,] 0.01208057029 0.4053658 0 0 0.0056
## [637,] -0.03522990388 0.7207918 0 0 0.0072
## [638,] -0.03107616241 0.6225049 0 0 0.0076
## [639,] -0.08893925852 1.5670453 0 0 0.0100
## [640,] -0.01994238694 0.9192121 0 0 0.0064
## [641,] -0.09979141641 1.6167202 0 0 0.0104
## [642,] 0.00301192289 0.7831058 0 0 0.0056
## [643,] -0.01498796711 0.6216625 0 0 0.0044
## [644,] -0.01073756966 2.6846074 0 0 0.0048
## [645,] -0.02376932075 0.5772823 0 0 0.0060
## [646,] -0.01338174923 1.2462357 0 0 0.0080
## [647,] 0.04366993378 2.4216642 0 0 0.0060
## [648,] -0.03844091259 0.8492515 0 0 0.0092
## [649,] -0.02472460111 0.9401103 0 0 0.0060
## [650,] 0.00409398198 1.8677951 0 0 0.0064
## [651,] 0.02616464799 0.9537302 0 0 0.0068
## [652,] -0.02923016742 0.8480949 0 0 0.0052
## [653,] -0.04730909252 0.9909860 0 0 0.0096
## [654,] 0.03721849136 1.8502211 0 0 0.0072
## [655,] -0.07622043567 1.8201368 0 0 0.0080
## [656,] 0.04238053369 1.4810121 0 0 0.0064
## [657,] -0.19512873616 3.6831856 0 0 0.0104
## [658,] 0.40896904136 5.8170387 0 0 0.0112
## [659,] -0.08495184234 1.9392471 0 0 0.0084
## [660,] 0.00184211962 0.5717520 0 0 0.0044
## [661,] 0.07120549368 2.7981661 0 0 0.0040
## [662,] -0.02996484072 0.6529241 0 0 0.0084
## [663,] -0.08084038072 1.4667883 0 0 0.0080
## [664,] -0.01015284388 0.5694142 0 0 0.0080
## [665,] -0.01915263732 0.5159555 0 0 0.00724.3.4 Predict fitted values for each individual
pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals4.3.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")
5 Linear models for each predictor
5.1 Screening the exposures
Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 3.06 ppb
lm_results <- data.frame()
for(i in 1:length(colnames(X.scaled))) {
lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
names(lm_df)[2] <- colnames(X.scaled)[i]
ad_lm <- lm(birth_weight ~ ., data = lm_df)
temp <- data.frame(exp = colnames(X.scaled)[i],
beta = summary(ad_lm)$coefficients[2,1],
beta.se = summary(ad_lm)$coefficients[2,2],
p.value = summary(ad_lm)$coefficients[2,4])
temp$lcl <- temp$beta - 1.96*temp$beta.se
temp$ucl <- temp$beta + 1.96*temp$beta.se
lm_results <- bind_rows(lm_results, temp)
rm(temp)
}
lm_resultswrite_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight.csv"))6 Linear model with the ozone predictor
The GAM model indicates a non-linear relationship between O3 and birth weight, None of the other exposures had a PIP > 0.5. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 3.06 ppb
lm_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(lm_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "latina_re" "black_re" "other_re"
## [9] "ed_no_hs" "ed_hs" "ed_aa" "ed_4yr"
## [13] "low_bmi" "ovwt_bmi" "obese_bmi" "concep_spring"
## [17] "concep_summer" "concep_fall" "concep_2010" "concep_2011"
## [21] "concep_2012" "concep_2013" "maternal_age" "any_smoker"
## [25] "smokeSH" "mean_cpss" "mean_epsd" "male"names(lm_df)[2] <- "mean_o3"
head(lm_df)bw_lm <- lm(birth_weight ~ mean_o3 +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = lm_df)
summary(bw_lm)##
## Call:
## lm(formula = birth_weight ~ mean_o3 + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2355.51 -278.44 45.25 307.30 1337.64
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2966.57 506.48 5.857 0.00000000667 ***
## mean_o3 -41.87 31.82 -1.316 0.18858
## lat -3090.26 18037.46 -0.171 0.86401
## lon 1479.17 8493.04 0.174 0.86178
## lat_lon_int -3725.55 21791.93 -0.171 0.86429
## latina_re -106.33 48.46 -2.194 0.02849 *
## black_re -298.56 52.30 -5.709 0.00000001560 ***
## other_re -105.34 70.18 -1.501 0.13369
## ed_no_hs 167.39 78.82 2.124 0.03397 *
## ed_hs 128.99 70.33 1.834 0.06698 .
## ed_aa 74.00 62.00 1.194 0.23298
## ed_4yr 77.21 52.15 1.481 0.13905
## low_bmi -107.61 94.73 -1.136 0.25630
## ovwt_bmi 35.21 41.25 0.853 0.39363
## obese_bmi 103.17 46.54 2.217 0.02691 *
## concep_spring -68.36 51.10 -1.338 0.18131
## concep_summer -26.46 76.79 -0.345 0.73048
## concep_fall -19.88 72.03 -0.276 0.78266
## concep_2010 208.72 507.45 0.411 0.68095
## concep_2011 196.49 508.25 0.387 0.69915
## concep_2012 167.27 509.07 0.329 0.74255
## concep_2013 256.08 507.38 0.505 0.61388
## maternal_age 66.63 22.54 2.957 0.00320 **
## any_smoker -132.39 65.27 -2.028 0.04284 *
## smokeSH -108.28 45.47 -2.382 0.01745 *
## mean_cpss 12.63 20.24 0.624 0.53282
## mean_epsd -53.22 20.58 -2.586 0.00987 **
## male 160.31 33.24 4.822 0.00000167727 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 492.1 on 869 degrees of freedom
## Multiple R-squared: 0.1531, Adjusted R-squared: 0.1268
## F-statistic: 5.817 on 27 and 869 DF, p-value: < 0.00000000000000022plot(bw_lm)## Warning: not plotting observations with leverage one:
## 1
7 Try a GAM with the ozone predictor
The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone to see about potential nonlinear effects
library(mgcv)## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## This is mgcv 1.8-31. For overview type 'help("mgcv-package")'.gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "latina_re" "black_re" "other_re"
## [9] "ed_no_hs" "ed_hs" "ed_aa" "ed_4yr"
## [13] "low_bmi" "ovwt_bmi" "obese_bmi" "concep_spring"
## [17] "concep_summer" "concep_fall" "concep_2010" "concep_2011"
## [21] "concep_2012" "concep_2013" "maternal_age" "any_smoker"
## [25] "smokeSH" "mean_cpss" "mean_epsd" "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)bw_gam <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df, method = "REML")
summary(bw_gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re +
## black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2860.915 484.120 5.910 0.00000000493 ***
## lat 3305.448 17276.689 0.191 0.84832
## lon -1550.961 8134.939 -0.191 0.84884
## lat_lon_int 3995.184 20872.788 0.191 0.84825
## latina_re -111.797 46.260 -2.417 0.01587 *
## black_re -305.145 49.965 -6.107 0.00000000153 ***
## other_re -80.542 67.161 -1.199 0.23077
## ed_no_hs 152.317 75.359 2.021 0.04356 *
## ed_hs 126.035 67.309 1.872 0.06148 .
## ed_aa 72.102 59.201 1.218 0.22358
## ed_4yr 82.343 49.892 1.650 0.09922 .
## low_bmi -114.274 90.823 -1.258 0.20865
## ovwt_bmi 46.224 39.434 1.172 0.24144
## obese_bmi 116.454 44.588 2.612 0.00916 **
## concep_spring -110.763 53.391 -2.075 0.03832 *
## concep_summer -42.155 79.128 -0.533 0.59435
## concep_fall -23.525 73.647 -0.319 0.74948
## concep_2010 296.927 485.690 0.611 0.54113
## concep_2011 268.758 486.592 0.552 0.58087
## concep_2012 303.572 487.442 0.623 0.53359
## concep_2013 400.030 486.002 0.823 0.41068
## maternal_age 52.121 21.593 2.414 0.01599 *
## any_smoker -153.447 62.528 -2.454 0.01432 *
## smokeSH -80.210 43.594 -1.840 0.06612 .
## mean_cpss 8.283 19.338 0.428 0.66850
## mean_epsd -51.781 19.683 -2.631 0.00867 **
## male 165.222 31.792 5.197 0.00000025295 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 5.969 7.22 12.2 0.00000000000000322 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.205 Deviance explained = 23.4%
## -REML = 6648.4 Scale est. = 2.2032e+05 n = 897jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight.jpeg"))
plot(bw_gam, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 28 GAM Sensitivity Analysis
The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.
Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.
library(mgcv)
quantile(X.scaled[,"mean_o3"], probs = c(0.025, 0.975))## 2.5% 97.5%
## -1.703410 1.852552q_2.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.025))
q_97.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.975))
gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "latina_re" "black_re" "other_re"
## [9] "ed_no_hs" "ed_hs" "ed_aa" "ed_4yr"
## [13] "low_bmi" "ovwt_bmi" "obese_bmi" "concep_spring"
## [17] "concep_summer" "concep_fall" "concep_2010" "concep_2011"
## [21] "concep_2012" "concep_2013" "maternal_age" "any_smoker"
## [25] "smokeSH" "mean_cpss" "mean_epsd" "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)gam_df2 <- gam_df %>%
filter(mean_o3 > q_2.5 & mean_o3 < q_97.5)
hist(gam_df2$mean_o3)
bw_gam2 <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df2, method = "REML")
summary(bw_gam2)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re +
## black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2802.17 471.71 5.940 0.00000000420 ***
## lat 8026.65 17448.88 0.460 0.64563
## lon -3777.43 8215.58 -0.460 0.64579
## lat_lon_int 9706.22 21080.80 0.460 0.64533
## latina_re -110.38 46.43 -2.377 0.01767 *
## black_re -293.91 49.93 -5.887 0.00000000573 ***
## other_re -83.29 66.77 -1.247 0.21263
## ed_no_hs 161.21 75.14 2.146 0.03220 *
## ed_hs 130.69 67.01 1.950 0.05148 .
## ed_aa 95.42 58.76 1.624 0.10476
## ed_4yr 69.48 49.67 1.399 0.16224
## low_bmi -137.85 89.78 -1.535 0.12507
## ovwt_bmi 62.86 39.47 1.593 0.11162
## obese_bmi 120.82 44.52 2.714 0.00679 **
## concep_spring -98.03 52.95 -1.851 0.06449 .
## concep_summer -37.90 77.82 -0.487 0.62641
## concep_fall -11.98 72.08 -0.166 0.86804
## concep_2010 368.19 473.13 0.778 0.43667
## concep_2011 356.27 474.25 0.751 0.45272
## concep_2012 369.42 475.07 0.778 0.43703
## concep_2013 451.57 473.60 0.953 0.34062
## maternal_age 55.20 21.46 2.573 0.01027 *
## any_smoker -187.21 62.04 -3.018 0.00263 **
## smokeSH -60.95 43.61 -1.398 0.16258
## mean_cpss 19.43 19.43 1.000 0.31757
## mean_epsd -54.42 19.71 -2.760 0.00590 **
## male 145.85 31.69 4.602 0.00000484264 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 4.003 4.977 4.962 0.000169 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.147 Deviance explained = 17.7%
## -REML = 6273.7 Scale est. = 2.0847e+05 n = 851jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v1.jpeg"))
plot(bw_gam2, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 29 GAM Sensitivity Analysis no. 2
Going to try the middle 90% of data as well, just in case
library(mgcv)
quantile(X.scaled[,"mean_o3"], probs = c(0.05, 0.95))## 5% 95%
## -1.568529 1.633168q_5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.05))
q_95 <- quantile(X.scaled[,"mean_o3"], probs = c(0.95))
gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "latina_re" "black_re" "other_re"
## [9] "ed_no_hs" "ed_hs" "ed_aa" "ed_4yr"
## [13] "low_bmi" "ovwt_bmi" "obese_bmi" "concep_spring"
## [17] "concep_summer" "concep_fall" "concep_2010" "concep_2011"
## [21] "concep_2012" "concep_2013" "maternal_age" "any_smoker"
## [25] "smokeSH" "mean_cpss" "mean_epsd" "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)gam_df3 <- gam_df %>%
filter(mean_o3 > q_5 & mean_o3 < q_95)
hist(gam_df3$mean_o3)
bw_gam3 <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df3, method = "REML")
summary(bw_gam3)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re +
## black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2789.77 467.39 5.969 0.00000000363 ***
## lat 6630.85 17798.05 0.373 0.709577
## lon -3116.35 8379.53 -0.372 0.710069
## lat_lon_int 8016.05 21502.25 0.373 0.709398
## latina_re -75.66 47.40 -1.596 0.110883
## black_re -283.65 50.64 -5.601 0.00000002952 ***
## other_re -77.60 67.72 -1.146 0.252221
## ed_no_hs 151.14 76.25 1.982 0.047813 *
## ed_hs 119.15 68.25 1.746 0.081238 .
## ed_aa 99.06 59.91 1.653 0.098670 .
## ed_4yr 59.19 50.50 1.172 0.241600
## low_bmi -189.87 90.70 -2.093 0.036641 *
## ovwt_bmi 41.89 40.01 1.047 0.295456
## obese_bmi 104.96 45.59 2.302 0.021599 *
## concep_spring -112.02 53.61 -2.090 0.036975 *
## concep_summer -41.70 77.81 -0.536 0.592186
## concep_fall -28.33 71.99 -0.393 0.694067
## concep_2010 425.40 468.81 0.907 0.364477
## concep_2011 417.60 470.03 0.888 0.374572
## concep_2012 401.55 470.80 0.853 0.393970
## concep_2013 482.86 469.32 1.029 0.303870
## maternal_age 57.53 21.91 2.626 0.008808 **
## any_smoker -207.03 62.48 -3.314 0.000963 ***
## smokeSH -62.64 44.24 -1.416 0.157159
## mean_cpss 16.20 19.69 0.823 0.410687
## mean_epsd -52.19 20.01 -2.608 0.009281 **
## male 133.62 32.16 4.155 0.00003613695 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 3.266 4.085 3.263 0.011 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.144 Deviance explained = 17.5%
## -REML = 5931.9 Scale est. = 2.0415e+05 n = 807jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v2.jpeg"))
plot(bw_gam3, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 210 GAM Sensitivity Analysis no. 3
For completeness, just the middle 75%
library(mgcv)
quantile(X.scaled[,"mean_o3"], probs = c(0.125, 0.875))## 12.5% 87.5%
## -1.210585 1.170781q_12.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.125))
q_87.5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.875))
gam_df <- as.data.frame(cbind(Y, X.scaled[, "mean_o3"], W.scaled2))
names(gam_df)## [1] "birth_weight" "V2" "lat" "lon"
## [5] "lat_lon_int" "latina_re" "black_re" "other_re"
## [9] "ed_no_hs" "ed_hs" "ed_aa" "ed_4yr"
## [13] "low_bmi" "ovwt_bmi" "obese_bmi" "concep_spring"
## [17] "concep_summer" "concep_fall" "concep_2010" "concep_2011"
## [21] "concep_2012" "concep_2013" "maternal_age" "any_smoker"
## [25] "smokeSH" "mean_cpss" "mean_epsd" "male"names(gam_df)[2] <- "mean_o3"
head(gam_df)gam_df4 <- gam_df %>%
filter(mean_o3 > q_12.5 & mean_o3 < q_87.5)
hist(gam_df4$mean_o3)
bw_gam4 <- gam(birth_weight ~ s(mean_o3) +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df4, method = "REML")
summary(bw_gam4)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3) + lat + lon + lat_lon_int + latina_re +
## black_re + other_re + ed_no_hs + ed_hs + ed_aa + ed_4yr +
## low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer +
## concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 +
## maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd +
## male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2867.26 455.27 6.298 0.000000000559 ***
## lat 9793.27 18535.77 0.528 0.597443
## lon -4589.21 8727.46 -0.526 0.599184
## lat_lon_int 11831.89 22393.58 0.528 0.597431
## latina_re -100.54 50.11 -2.006 0.045240 *
## black_re -301.84 53.69 -5.622 0.000000028087 ***
## other_re -72.33 71.51 -1.011 0.312204
## ed_no_hs 127.69 83.09 1.537 0.124851
## ed_hs 142.01 72.89 1.948 0.051816 .
## ed_aa 70.48 63.07 1.117 0.264207
## ed_4yr 50.59 52.98 0.955 0.340011
## low_bmi -273.34 98.57 -2.773 0.005714 **
## ovwt_bmi 56.64 42.89 1.320 0.187142
## obese_bmi 115.88 49.29 2.351 0.019028 *
## concep_spring -134.92 55.91 -2.413 0.016100 *
## concep_summer -94.96 81.22 -1.169 0.242776
## concep_fall -22.23 71.43 -0.311 0.755690
## concep_2010 382.97 456.13 0.840 0.401439
## concep_2011 425.19 457.65 0.929 0.353196
## concep_2012 374.58 458.34 0.817 0.414081
## concep_2013 473.94 457.23 1.037 0.300331
## maternal_age 50.32 23.58 2.134 0.033199 *
## any_smoker -208.65 67.53 -3.090 0.002090 **
## smokeSH -56.16 46.26 -1.214 0.225248
## mean_cpss 12.44 22.00 0.565 0.571985
## mean_epsd -58.12 21.99 -2.643 0.008410 **
## male 125.63 34.25 3.668 0.000265 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3) 1.002 1.003 2.494 0.114
##
## R-sq.(adj) = 0.146 Deviance explained = 18%
## -REML = 4882.2 Scale est. = 1.9156e+05 n = 671jpeg(here::here("Figs", "Ozone_GAM_Birth_Weight_Sensitivity_v3.jpeg"))
plot(bw_gam4, main = "GAM with a smoothing term for ozone",
xlab = "Ozone (scaled)", ylab = "Change in birth weight (g)")
dev.off()## quartz_off_screen
## 2